pdf2htmlEX/demo/cheat1.page

<div class="pd w0 h0"><div id="pf1" class="pf" data-page-no="1"><div class="pc pc1"><img class="bi x0 y0 w1 h1" alt="" src="data:image/png;base64,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"/><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Theoretical<span class="_ _0"> </span>Computer<span class="_ _0"> </span>Science<span class="_ _0"> </span>Cheat<span class="_ _0"> </span>Sheet</div><div class="t m0 x2 h3 y2 ff2 fs0 fc0 sc0 ls0 ws0">Definitions<span class="_ _1"> </span>Series</div><div class="t m0 x3 h4 y3 ff3 fs0 fc0 sc0 ls0 ws0">f<span class="_ _2"></span><span class="ff2">(</span>n<span class="ff2 ls1">)=</span>O<span class="_ _3"></span><span class="ff2">(</span>g<span class="_ _3"></span><span class="ff2">(</span>n<span class="ff2">))<span class="_ _4"> </span>iff<span class="_ _0"> </span><span class="ff4">∃<span class="_ _0"> </span></span>positiv<span class="_ _5"></span>e<span class="_ _0"> </span><span class="ff3">c,<span class="_ _6"> </span>n</span></span></div><div class="t m0 x4 h5 y4 ff5 fs1 fc0 sc0 ls0 ws0">0</div><div class="t m0 x5 h3 y3 ff2 fs0 fc0 sc0 ls0 ws0">suc<span class="_ _5"></span>h<span class="_ _0"> </span>that</div><div class="t m0 x6 h4 y5 ff2 fs0 fc0 sc0 ls0 ws0">0<span class="_ _7"> </span><span class="ff4">≤<span class="_ _7"> </span><span class="ff3">f<span class="_ _2"></span></span></span>(<span class="ff3">n</span>)<span class="_ _7"> </span><span class="ff4">≤<span class="_ _7"> </span><span class="ff3">cg<span class="_ _3"></span></span></span>(<span class="ff3">n</span>) <span class="ff4">∀<span class="ff3">n<span class="_ _7"> </span></span>≥<span class="_ _7"> </span><span class="ff3">n</span></span></div><div class="t m0 x7 h5 y6 ff5 fs1 fc0 sc0 ls0 ws0">0</div><div class="t m0 x8 h3 y7 ff2 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x9 h5 y8 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 xa h6 y9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xb h5 ya ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 xc h3 y6 ff3 fs0 fc0 sc0 ls0 ws0">i<span class="_ _7"> </span><span class="ff2">=</span></div><div class="t m0 xd h3 yb ff3 fs0 fc0 sc0 ls0 ws0">n<span class="ff2">(</span>n<span class="_ _8"> </span><span class="ff2 ls2">+1<span class="_ _9"></span>)</span></div><div class="t m0 xe h3 yc ff2 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 xf h3 y6 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x10 h5 y8 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x11 h6 y9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x12 h5 ya ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 x13 h3 y6 ff3 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x14 h5 yd ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x15 h3 y6 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x16 h3 yb ff3 fs0 fc0 sc0 ls0 ws0">n<span class="ff2">(</span>n<span class="_ _8"> </span><span class="ff2">+<span class="_ _8"> </span>1)(2</span>n<span class="_ _8"> </span><span class="ff2 ls2">+1<span class="_ _9"></span>)</span></div><div class="t m0 x17 h3 yc ff2 fs0 fc0 sc0 ls0 ws0">6</div><div class="t m0 x18 h3 y6 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x19 h5 y8 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x1a h6 y9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x1b h5 ya ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 x1c h3 y6 ff3 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x1d h5 yd ff5 fs1 fc0 sc0 ls0 ws0">3</div><div class="t m0 x1e h3 y6 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x1f h3 yb ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x20 h5 ye ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x21 h3 yf ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff3">n<span class="_ _8"> </span></span><span class="ls2">+1<span class="_ _9"></span>)</span></div><div class="t m0 x22 h5 ye ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x23 h3 yc ff2 fs0 fc0 sc0 ls0 ws0">4</div><div class="t m0 x24 h3 y6 ff3 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x25 h3 y10 ff2 fs0 fc0 sc0 ls0 ws0">In general:</div><div class="t m0 xa h5 y11 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x26 h6 y12 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x27 h5 y13 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 x28 h3 y14 ff3 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 xc h5 y15 ff6 fs1 fc0 sc0 ls0 ws0">m</div><div class="t m0 x29 h3 y14 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x2a h3 y16 ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 x2b h3 y17 ff3 fs0 fc0 sc0 ls0 ws0">m<span class="_ _8"> </span><span class="ff2 ls2">+1</span></div><div class="t m0 x2c h6 y18 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x2d h3 y14 ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff3">n<span class="_ _8"> </span></span><span class="ls2">+1<span class="_ _9"></span>)</span></div><div class="t m0 x2e h5 y15 ff6 fs1 fc0 sc0 ls0 ws0">m<span class="ff5">+1</span></div><div class="t m0 x2f h4 y14 ff4 fs0 fc0 sc0 ls0 ws0">−<span class="_ _8"> </span><span class="ff2">1<span class="_ _8"> </span></span>−</div><div class="t m0 x30 h5 y11 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x31 h6 y12 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x32 h5 y13 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 x33 h6 y19 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x34 h3 y14 ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff3">i<span class="_ _8"> </span></span><span class="ls2">+1<span class="_ _9"></span>)</span></div><div class="t m0 x35 h5 y15 ff6 fs1 fc0 sc0 ls0 ws0">m<span class="ff5">+1</span></div><div class="t m0 x36 h4 y14 ff4 fs0 fc0 sc0 ls0 ws0">−<span class="_ _8"> </span><span class="ff3">i</span></div><div class="t m0 x1c h5 y15 ff6 fs1 fc0 sc0 ls0 ws0">m<span class="ff5">+1</span></div><div class="t m0 x37 h4 y14 ff4 fs0 fc0 sc0 ls0 ws0">−<span class="_ _8"> </span><span class="ff2">(<span class="ff3">m<span class="_ _8"> </span></span><span class="ls2">+1<span class="_ _9"></span>)<span class="_ _9"></span><span class="ff3 ls0">i</span></span></span></div><div class="t m0 x38 h5 y15 ff6 fs1 fc0 sc0 ls0 ws0">m</div><div class="t m0 x39 h6 y19 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x3a h6 y18 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x26 h5 y1a ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff8">−<span class="ff5">1</span></span></div><div class="t m0 x26 h6 y1b ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x26 h5 y1c ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 x28 h3 y1d ff3 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 xc h5 y1e ff6 fs1 fc0 sc0 ls0 ws0">m</div><div class="t m0 x29 h3 y1d ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x2a h3 y1f ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 x2b h3 y20 ff3 fs0 fc0 sc0 ls0 ws0">m<span class="_ _8"> </span><span class="ff2 ls2">+1</span></div><div class="t m0 x2d h5 y1a ff6 fs1 fc0 sc0 ls0 ws0">m</div><div class="t m0 x3b h6 y1b ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x3b h5 y1c ff6 fs1 fc0 sc0 ls0 ws0">k<span class="ff5">=0</span></div><div class="t m0 x3c h6 y21 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x3d h3 y22 ff3 fs0 fc0 sc0 ls0 ws0">m<span class="_ _8"> </span><span class="ff2 ls2">+1</span></div><div class="t m0 x2e h3 y20 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x3e h6 y21 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x3f h3 y1d ff3 fs0 fc0 sc0 ls0 ws0">B</div><div class="t m0 x40 h5 y23 ff6 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x41 h3 y1d ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x42 h5 y1e ff6 fs1 fc0 sc0 ls0 ws0">m<span class="ff5">+1<span class="ff8">−</span></span>k</div><div class="t m0 x43 h3 y1d ff3 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x25 h3 y24 ff2 fs0 fc0 sc0 ls0 ws0">Geometric series:</div><div class="t m0 xb h5 y25 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x27 h6 y26 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x44 h5 y27 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=0</span></div><div class="t m0 x45 h3 y28 ff3 fs0 fc0 sc0 ls0 ws0">c</div><div class="t m0 xc h5 y29 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x46 h3 y28 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 xd h3 y2a ff3 fs0 fc0 sc0 ls0 ws0">c</div><div class="t m0 x47 h5 y2b ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff5">+1</span></div><div class="t m0 x48 h4 y2c ff4 fs0 fc0 sc0 ls0 ws0">−<span class="_ _8"> </span><span class="ff2">1</span></div><div class="t m0 x49 h4 y2d ff3 fs0 fc0 sc0 ls0 ws0">c<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1</span></span></div><div class="t m0 xf h4 y2e ff3 fs0 fc0 sc0 ls3 ws0">,c<span class="_ _a"></span><span class="ff4 ls0"><span class="ff2 ls1">=1<span class="_ _b"></span><span class="ff3 ls0">,</span></span></span></div><div class="t m0 x4a h5 y25 ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 x16 h6 y26 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x16 h5 y27 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=0</span></div><div class="t m0 x42 h3 y28 ff3 fs0 fc0 sc0 ls0 ws0">c</div><div class="t m0 x4b h5 y29 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x4c h3 y28 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x4d h3 y2a ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 x33 h4 y2d ff2 fs0 fc0 sc0 ls0 ws0">1<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff3">c</span></span></div><div class="t m0 x4e h3 y2e ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x4f h5 y25 ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 x18 h6 y26 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x50 h5 y27 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 x36 h3 y28 ff3 fs0 fc0 sc0 ls0 ws0">c</div><div class="t m0 x51 h5 y29 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x52 h3 y28 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x53 h3 y2a ff3 fs0 fc0 sc0 ls0 ws0">c</div><div class="t m0 x54 h4 y2d ff2 fs0 fc0 sc0 ls0 ws0">1<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff3">c</span></span></div><div class="t m0 x55 h4 y2e ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _c"> </span><span class="ff4">|</span>c<span class="ff4">|<span class="_ _7"> </span></span>&lt;<span class="_ _7"> </span><span class="ff2">1</span>,</div><div class="t m0 x56 h5 y2f ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x25 h6 y30 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x57 h5 y31 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=0</span></div><div class="t m0 x58 h3 y32 ff3 fs0 fc0 sc0 ls0 ws0">ic</div><div class="t m0 x59 h5 y33 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x46 h3 y32 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x5a h3 y34 ff3 fs0 fc0 sc0 ls0 ws0">nc</div><div class="t m0 x5b h5 y35 ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff5">+2</span></div><div class="t m0 x5c h4 y36 ff4 fs0 fc0 sc0 ls0 ws0">−<span class="_ _8"> </span><span class="ff2">(<span class="ff3">n<span class="_ _8"> </span></span><span class="ls2">+1<span class="_ _9"></span>)<span class="_ _9"></span><span class="ff3 ls0">c</span></span></span></div><div class="t m0 x5d h5 y35 ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff5">+1</span></div><div class="t m0 x5e h3 y36 ff2 fs0 fc0 sc0 ls0 ws0">+<span class="_ _8"> </span><span class="ff3">c</span></div><div class="t m0 x5f h4 y37 ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff3">c<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span></span></span>1)</div><div class="t m0 x2e h5 y38 ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x42 h4 y32 ff3 fs0 fc0 sc0 ls3 ws0">,c<span class="_ _a"></span><span class="ff4 ls0"><span class="ff2 ls1">=1<span class="_ _b"></span><span class="ff3 ls0">,</span></span></span></div><div class="t m0 x35 h5 y2f ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 x60 h6 y30 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x61 h5 y31 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=0</span></div><div class="t m0 x62 h3 y32 ff3 fs0 fc0 sc0 ls0 ws0">ic</div><div class="t m0 x36 h5 y33 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x63 h3 y32 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x37 h3 y34 ff3 fs0 fc0 sc0 ls0 ws0">c</div><div class="t m0 x64 h4 y37 ff2 fs0 fc0 sc0 ls0 ws0">(1<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff3">c</span></span>)</div><div class="t m0 x65 h5 y38 ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x66 h4 y32 ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _c"> </span><span class="ff4">|</span>c<span class="ff4">|<span class="_ _7"> </span></span>&lt;<span class="_ _7"> </span><span class="ff2">1</span>.</div><div class="t m0 x25 h3 y39 ff2 fs0 fc0 sc0 ls0 ws0">Harmonic series:</div><div class="t m0 x47 h3 y3a ff3 fs0 fc0 sc0 ls0 ws0">H</div><div class="t m0 x67 h5 y3b ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x68 h3 y3c ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x2d h5 y3d ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x2c h6 y3e ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x3b h5 y3f ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 x3c h3 y40 ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 x69 h3 y41 ff3 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x6a h3 y42 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x6b h5 y3d ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x15 h6 y3e ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x15 h5 y3f ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 x6c h3 y3c ff3 fs0 fc0 sc0 ls0 ws0">iH</div><div class="t m0 x42 h5 y3b ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x31 h3 y3c ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x17 h3 y40 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="ff2">(</span>n<span class="_ _8"> </span><span class="ff2 ls2">+1<span class="_ _9"></span>)</span></div><div class="t m0 x6d h3 y41 ff2 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 x35 h3 y42 ff3 fs0 fc0 sc0 ls0 ws0">H</div><div class="t m0 x6e h5 y3b ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x6f h4 y3c ff4 fs0 fc0 sc0 ls0 ws0">−</div><div class="t m0 x70 h4 y40 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="ff2">(</span>n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1)</span></span></div><div class="t m0 x1e h3 y41 ff2 fs0 fc0 sc0 ls0 ws0">4</div><div class="t m0 x21 h3 y42 ff3 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x71 h5 y43 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x27 h6 y44 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x44 h5 y45 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 x45 h3 y46 ff3 fs0 fc0 sc0 ls0 ws0">H</div><div class="t m0 x72 h5 y47 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x73 h3 y46 ff2 fs0 fc0 sc0 ls1 ws0">=(<span class="_ _b"></span><span class="ff3 ls0">n<span class="_ _8"> </span><span class="ff2 ls2">+1<span class="_ _9"></span>)<span class="_ _9"></span><span class="ff3 ls0">H</span></span></span></div><div class="t m0 x74 h5 y47 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x75 h4 y46 ff4 fs0 fc0 sc0 ls0 ws0">−<span class="_ _8"> </span><span class="ff3">n,</span></div><div class="t m0 x2f h5 y43 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x3e h6 y44 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x3e h5 y45 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 x76 h6 y48 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x42 h3 y49 ff3 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x77 h3 y4a ff3 fs0 fc0 sc0 ls0 ws0">m</div><div class="t m0 x31 h6 y48 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x78 h3 y46 ff3 fs0 fc0 sc0 ls0 ws0">H</div><div class="t m0 x33 h5 y47 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x43 h3 y46 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x79 h6 y4b ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x7a h3 y4c ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff2 ls2">+1</span></div><div class="t m0 x7b h3 y4d ff3 fs0 fc0 sc0 ls0 ws0">m<span class="_ _8"> </span><span class="ff2 ls2">+1</span></div><div class="t m0 x6f h6 y4b ff7 fs0 fc0 sc0 ls4 ws0"></div><div class="t m0 x1c h3 y46 ff3 fs0 fc0 sc0 ls0 ws0">H</div><div class="t m0 x54 h5 y47 ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff5">+1</span></div><div class="t m0 x7c h4 y46 ff4 fs0 fc0 sc0 ls0 ws0">−</div><div class="t m0 x7d h3 y49 ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 x7e h3 y4d ff3 fs0 fc0 sc0 ls0 ws0">m<span class="_ _8"> </span><span class="ff2 ls2">+1</span></div><div class="t m0 x22 h6 y4b ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x7f h3 y46 ff3 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x80 h4 y4e ff3 fs0 fc0 sc0 ls0 ws0">f<span class="_ _2"></span><span class="ff2">(</span>n<span class="ff2 ls1">)=Ω<span class="_ _b"></span>(<span class="_ _b"></span><span class="ff3 ls0">g<span class="_ _3"></span><span class="ff2">(</span>n<span class="ff2">))<span class="_ _d"> </span>iff<span class="_ _0"> </span><span class="ff4">∃<span class="_ _0"> </span></span>positiv<span class="_ _5"></span>e<span class="_ _0"> </span><span class="ff3">c,<span class="_ _6"> </span>n</span></span></span></span></div><div class="t m0 x4 h5 y4f ff5 fs1 fc0 sc0 ls0 ws0">0</div><div class="t m0 x5 h3 y4e ff2 fs0 fc0 sc0 ls0 ws0">suc<span class="_ _5"></span>h<span class="_ _0"> </span>that</div><div class="t m0 x6 h4 y50 ff3 fs0 fc0 sc0 ls0 ws0">f<span class="_ _2"></span><span class="ff2">(</span>n<span class="ff2">)<span class="_ _7"> </span><span class="ff4">≥<span class="_ _7"> </span></span></span>cg<span class="_ _3"></span><span class="ff2">(</span>n<span class="ff2">)<span class="_ _7"> </span><span class="ff4">≥<span class="_ _7"> </span></span>0 <span class="ff4">∀</span></span>n<span class="_ _7"> </span><span class="ff4">≥<span class="_ _7"> </span></span>n</div><div class="t m0 x7 h5 y51 ff5 fs1 fc0 sc0 ls0 ws0">0</div><div class="t m0 x8 h3 y52 ff2 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x80 h3 y53 ff3 fs0 fc0 sc0 ls0 ws0">f<span class="_ _2"></span><span class="ff2">(</span>n<span class="ff2 ls1">)=Θ<span class="_ _b"></span>(<span class="_ _b"></span><span class="ff3 ls0">g<span class="_ _3"></span><span class="ff2">(</span>n<span class="ff2">))<span class="_ _d"> </span>iff<span class="_ _e"> </span></span>f<span class="_ _2"></span><span class="ff2">(</span>n<span class="ff2 ls5">)=</span>O<span class="_ _3"></span><span class="ff2">(</span>g<span class="_ _3"></span><span class="ff2">(</span>n<span class="ff2">))<span class="_ _f"> </span>and</span></span></span></div><div class="t m0 x6 h3 y54 ff3 fs0 fc0 sc0 ls0 ws0">f<span class="_ _2"></span><span class="ff2">(</span>n<span class="ff2 ls1">)=Ω<span class="_ _b"></span>(<span class="_ _b"></span><span class="ff3 ls0">g<span class="_ _3"></span><span class="ff2">(</span>n<span class="ff2">)).</span></span></span></div><div class="t m0 x81 h3 y55 ff3 fs0 fc0 sc0 ls0 ws0">f<span class="_ _2"></span><span class="ff2">(</span>n<span class="ff2 ls1">)=</span>o<span class="ff2">(</span>g<span class="_ _3"></span><span class="ff2">(</span>n<span class="ff2">))<span class="_ _d"> </span>iff<span class="_ _7"> </span>lim</span></div><div class="t m0 x82 h5 y56 ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff8">→∞</span></div><div class="t m0 x83 h3 y55 ff3 fs0 fc0 sc0 ls0 ws0">f<span class="_ _2"></span><span class="ff2">(</span>n<span class="ff2">)</span>/g<span class="_ _3"></span><span class="ff2">(</span>n<span class="ff2 ls1">)=0<span class="_ _b"></span>.</span></div><div class="t m0 x84 h3 y57 ff2 fs0 fc0 sc0 ls0 ws0">lim</div><div class="t m0 x85 h5 y58 ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff8">→∞</span></div><div class="t m0 x86 h3 y57 ff3 fs0 fc0 sc0 ls0 ws0">a</div><div class="t m0 x87 h5 y59 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x88 h4 y57 ff2 fs0 fc0 sc0 ls0 ws0">=<span class="_ _7"> </span><span class="ff3">a<span class="_ _10"> </span></span>iff<span class="_ _11"> </span><span class="ff4">∀<span class="ff3 ls6">&gt;</span></span>0,<span class="_ _12"> </span><span class="ff4">∃<span class="ff3">n</span></span></div><div class="t m0 x89 h5 y59 ff5 fs1 fc0 sc0 ls0 ws0">0</div><div class="t m0 x8a h3 y57 ff2 fs0 fc0 sc0 ls0 ws0">suc<span class="_ _5"></span>h<span class="_ _11"> </span>that</div><div class="t m0 x6 h4 y5a ff4 fs0 fc0 sc0 ls0 ws0">|<span class="ff3">a</span></div><div class="t m0 x8b h5 y5b ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x8c h4 y5c ff4 fs0 fc0 sc0 ls0 ws0">−<span class="_ _8"> </span><span class="ff3">a</span>|<span class="_ _7"> </span><span class="ff3 ls1">&lt;<span class="_ _b"></span><span class="ff2 ls0">, <span class="ff4">∀<span class="ff3">n<span class="_ _7"> </span></span>≥<span class="_ _7"> </span><span class="ff3">n</span></span></span></span></div><div class="t m0 x8d h5 y5b ff5 fs1 fc0 sc0 ls0 ws0">0</div><div class="t m0 x8e h3 y5c ff2 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x8f h4 y5d ff2 fs0 fc0 sc0 ls0 ws0">sup<span class="_ _6"> </span><span class="ff3">S<span class="_ _13"> </span></span>least<span class="_ _0"> </span><span class="ff3">b<span class="_ _14"> </span><span class="ff4">∈<span class="_ _14"> </span><span class="ff9">R<span class="_ _0"> </span></span></span></span>suc<span class="_ _5"></span>h<span class="_ _0"> </span>that <span class="ff3">b <span class="ff4">≥<span class="_ _0"> </span></span>s<span class="_ _5"></span><span class="ff2">,</span></span></div><div class="t m0 x6 h4 y5e ff4 fs0 fc0 sc0 ls0 ws0">∀<span class="ff3">s<span class="_ _7"> </span></span>∈<span class="_ _7"> </span><span class="ff3">S<span class="_ _15"></span><span class="ff2">.</span></span></div><div class="t m0 x90 h4 y5f ff2 fs0 fc0 sc0 ls0 ws0">inf<span class="_ _8"> </span><span class="ff3">S<span class="_ _16"> </span></span>greatest<span class="_ _14"> </span><span class="ff3">b<span class="_ _7"> </span><span class="ff4">∈<span class="_ _7"> </span><span class="ff9">R<span class="_ _14"> </span></span></span></span>suc<span class="_ _5"></span>h that<span class="_ _7"> </span><span class="ff3">b<span class="_ _7"> </span><span class="ff4">≤</span></span></div><div class="t m0 x6 h4 y60 ff3 fs0 fc0 sc0 ls0 ws0">s<span class="ff2">, <span class="ff4">∀</span></span>s<span class="_ _7"> </span><span class="ff4">∈<span class="_ _7"> </span></span>S<span class="_ _15"></span><span class="ff2">.</span></div><div class="t m0 x91 h3 y61 ff2 fs0 fc0 sc0 ls0 ws0">lim<span class="_ _6"> </span>inf</div><div class="t m0 x92 h5 y62 ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff8">→∞</span></div><div class="t m0 x88 h3 y61 ff3 fs0 fc0 sc0 ls0 ws0">a</div><div class="t m0 x93 h5 y63 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x94 h3 y61 ff2 fs0 fc0 sc0 ls0 ws0">lim</div><div class="t m0 x6 h5 y62 ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff8">→∞</span></div><div class="t m0 x95 h4 y61 ff2 fs0 fc0 sc0 ls0 ws0">inf<span class="_ _15"></span><span class="ff4">{<span class="ff3">a</span></span></div><div class="t m0 x96 h5 y63 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x97 h4 y61 ff4 fs0 fc0 sc0 ls0 ws0">|<span class="_ _7"> </span><span class="ff3">i<span class="_ _7"> </span></span>≥<span class="_ _7"> </span><span class="ff3">n,<span class="_ _6"> </span>i<span class="_ _7"> </span></span>∈<span class="_ _7"> </span><span class="ff9">N</span>}<span class="ff2">.</span></div><div class="t m0 x84 h3 y64 ff2 fs0 fc0 sc0 ls0 ws0">lim<span class="_ _6"> </span>sup</div><div class="t m0 x98 h5 y65 ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff8">→∞</span></div><div class="t m0 x88 h3 y64 ff3 fs0 fc0 sc0 ls0 ws0">a</div><div class="t m0 x93 h5 y66 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x94 h3 y64 ff2 fs0 fc0 sc0 ls0 ws0">lim</div><div class="t m0 x6 h5 y67 ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff8">→∞</span></div><div class="t m0 x95 h4 y64 ff2 fs0 fc0 sc0 ls0 ws0">sup<span class="ff4">{<span class="ff3">a</span></span></div><div class="t m0 x83 h5 y66 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x99 h4 y64 ff4 fs0 fc0 sc0 ls0 ws0">|<span class="_ _7"> </span><span class="ff3">i<span class="_ _7"> </span></span>≥<span class="_ _7"> </span><span class="ff3">n,<span class="_ _6"> </span>i<span class="_ _7"> </span></span>∈<span class="_ _7"> </span><span class="ff9">N</span>}<span class="ff2">.</span></div><div class="t m0 x9a h6 y44 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x86 h5 y68 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x86 h5 y69 ff6 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x87 h6 y44 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x6 h3 y6a ff2 fs0 fc0 sc0 ls0 ws0">Com<span class="_ _5"></span>binations:<span class="_ _17"> </span>Size<span class="_ _11"> </span><span class="ff3">k<span class="_ _11"> </span></span>sub-</div><div class="t m0 x6 h3 y6b ff2 fs0 fc0 sc0 ls0 ws0">sets of a size <span class="ff3">n </span>set.</div><div class="t m0 x9a h6 y6c ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x86 h5 y6d ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x86 h5 y6e ff6 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x87 h6 y6c ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x6 h3 y6f ff2 fs0 fc0 sc0 ls0 ws0">Stirling<span class="_ _0"> </span>n<span class="_ _5"></span>um<span class="_ _5"></span>b<span class="_ _3"></span>ers<span class="_ _0"> </span>(1st<span class="_ _0"> </span>kind):</div><div class="t m0 x6 h3 y70 ff2 fs0 fc0 sc0 ls0 ws0">Arrangemen<span class="_ _5"></span>ts<span class="_ _11"> </span>of<span class="_ _11"> </span>an<span class="_ _11"> </span><span class="ff3">n<span class="_ _11"> </span></span>ele-</div><div class="t m0 x6 h3 y71 ff2 fs0 fc0 sc0 ls0 ws0">men<span class="_ _5"></span>t set into <span class="ff3">k </span>cycles.</div><div class="t m0 x25 h2 y72 ff1 fs0 fc0 sc0 ls0 ws0">1.</div><div class="t m0 x9b h6 y73 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x9c h3 y74 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x9c h3 y75 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x72 h6 y73 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x9d h3 y72 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x9e h3 y74 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="ff2">!</span></div><div class="t m0 x49 h4 y75 ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff3">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span></span>k<span class="_ _3"></span></span>)!<span class="ff3">k<span class="_ _3"></span></span>!</div><div class="t m0 x11 h3 y76 ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _18"> </span><span class="ff1">2.</span></div><div class="t m0 x41 h5 y77 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x40 h6 y78 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x40 h5 y79 ff6 fs1 fc0 sc0 ls0 ws0">k<span class="ff5">=0</span></div><div class="t m0 x9f h6 y73 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xa0 h3 y74 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xa0 h3 y75 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x17 h6 y73 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x43 h3 y72 ff2 fs0 fc0 sc0 ls1 ws0">=2</div><div class="t m0 x4e h5 y6e ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 xa1 h3 y72 ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _18"> </span><span class="ff1">3.</span></div><div class="t m0 x64 h6 y73 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xa2 h3 y74 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xa2 h3 y75 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xa3 h6 y73 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x20 h3 y72 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 xa4 h6 y73 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xa5 h3 y74 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xa6 h4 y75 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span></span>k</div><div class="t m0 x24 h6 y73 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xa7 h3 y72 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x25 h2 y7a ff1 fs0 fc0 sc0 ls0 ws0">4.</div><div class="t m0 x9b h6 y7b ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x9c h3 y7c ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x9c h3 y7d ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x72 h6 y7b ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x9d h3 y7a ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x49 h3 y7c ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x49 h3 y7e ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xe h6 y7f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x48 h4 y80 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1</span></span></div><div class="t m0 x48 h4 y7e ff3 fs0 fc0 sc0 ls0 ws0">k<span class="_ _7"> </span><span class="ff4">−<span class="_ _8"></span><span class="ff2">1</span></span></div><div class="t m0 xa8 h6 y7f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x12 h3 y81 ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _19"> </span><span class="ff1">5.</span></div><div class="t m0 x4e h6 y7f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x60 h3 y80 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x60 h3 y7e ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xa9 h6 y7f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x62 h3 y81 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x19 h6 y7f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x52 h4 y80 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1</span></span></div><div class="t m0 x64 h3 y7e ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x37 h6 y7f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x20 h3 y81 ff2 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 xa4 h6 y7f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xa6 h4 y80 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1</span></span></div><div class="t m0 x7d h4 y7e ff3 fs0 fc0 sc0 ls0 ws0">k<span class="_ _7"> </span><span class="ff4">−<span class="_ _8"></span><span class="ff2">1</span></span></div><div class="t m0 x24 h6 y7f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xa7 h3 y81 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x25 h2 y82 ff1 fs0 fc0 sc0 ls0 ws0">6.</div><div class="t m0 x9b h6 y83 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xc h3 y84 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x9c h3 y85 ff3 fs0 fc0 sc0 ls0 ws0">m</div><div class="t m0 x46 h6 y83 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x47 h3 y84 ff3 fs0 fc0 sc0 ls0 ws0">m</div><div class="t m0 xaa h3 y85 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x2a h6 y83 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x48 h3 y82 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 xab h6 y83 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xac h3 y84 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xac h3 y85 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xad h6 y83 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xae h4 y84 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span></span>k</div><div class="t m0 xaf h4 y85 ff3 fs0 fc0 sc0 ls0 ws0">m<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span></span>k</div><div class="t m0 x3f h6 y83 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x6c h3 y82 ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _1a"> </span><span class="ff1">7.</span></div><div class="t m0 xa1 h5 y86 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x4e h6 y87 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x4e h5 y88 ff6 fs1 fc0 sc0 ls0 ws0">k<span class="ff5">=0</span></div><div class="t m0 xb0 h6 y89 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x62 h3 y8a ff3 fs0 fc0 sc0 ls0 ws0">r<span class="_ _7"> </span><span class="ff2">+<span class="_ _8"> </span></span>k</div><div class="t m0 x36 h3 y8b ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xb1 h6 y89 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x1e h3 y8c ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x1f h6 y89 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xb2 h3 y8a ff3 fs0 fc0 sc0 ls0 ws0">r<span class="_ _7"> </span><span class="ff2">+<span class="_ _8"> </span></span>n<span class="_ _8"> </span><span class="ff2 ls2">+1</span></div><div class="t m0 x7d h3 y8b ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x24 h6 y89 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xa7 h3 y8c ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x25 h2 y8d ff1 fs0 fc0 sc0 ls0 ws0">8.</div><div class="t m0 x28 h5 y8e ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x9b h6 y8f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x9b h5 y90 ff6 fs1 fc0 sc0 ls0 ws0">k<span class="ff5">=0</span></div><div class="t m0 x46 h6 y91 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xb3 h3 y92 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x9d h3 y93 ff3 fs0 fc0 sc0 ls0 ws0">m</div><div class="t m0 x47 h6 y91 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xe h3 y94 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 xb4 h6 y91 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x2d h3 y92 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff2 ls2">+1</span></div><div class="t m0 xab h3 y93 ff3 fs0 fc0 sc0 ls0 ws0">m<span class="_ _8"> </span><span class="ff2 ls2">+1</span></div><div class="t m0 xb5 h6 y91 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x2e h3 y94 ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _1b"> </span><span class="ff1">9.</span></div><div class="t m0 x7b h5 y8e ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 xb6 h6 y8f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xb6 h5 y90 ff6 fs1 fc0 sc0 ls0 ws0">k<span class="ff5">=0</span></div><div class="t m0 xa9 h6 y91 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xb7 h3 y92 ff3 fs0 fc0 sc0 ls0 ws0">r</div><div class="t m0 xb7 h3 y93 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xb8 h6 y91 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xb9 h3 y92 ff3 fs0 fc0 sc0 ls0 ws0">s</div><div class="t m0 x52 h4 y93 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span></span>k</div><div class="t m0 x37 h6 y91 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x55 h3 y94 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x66 h6 y91 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x7d h3 y92 ff3 fs0 fc0 sc0 ls0 ws0">r<span class="_ _7"> </span><span class="ff2">+<span class="_ _8"> </span></span>s</div><div class="t m0 xba h3 y93 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x24 h6 y91 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xa7 h3 y94 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x25 h2 y95 ff1 fs0 fc0 sc0 ls0 ws0">10.</div><div class="t m0 x45 h6 y96 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x72 h3 y97 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x72 h3 y98 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x73 h6 y96 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x2b h4 y95 ff2 fs0 fc0 sc0 ls1 ws0">=(<span class="_ _b"></span><span class="ff4 ls0">−<span class="ff2">1)</span></span></div><div class="t m0 xab h5 y99 ff6 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 xf h6 y9a ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xa8 h4 y9b ff3 fs0 fc0 sc0 ls0 ws0">k<span class="_ _7"> </span><span class="ff4">−<span class="_ _8"></span></span>n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"></span><span class="ff2">1</span></span></div><div class="t m0 xae h3 y9c ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x2f h6 y9a ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x4a h3 y9d ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _1c"> </span><span class="ff1">11.</span></div><div class="t m0 xbb h6 y9a ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x54 h3 y9b ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x54 h3 y9c ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 xbc h6 y9a ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x7c h3 y9d ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 xbd h6 y9a ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xbe h3 y9b ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xbe h3 y9c ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xbf h6 y9a ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xc0 h3 y9d ff2 fs0 fc0 sc0 ls1 ws0">=1<span class="_ _b"></span><span class="ff3 ls0">,</span></div><div class="t m0 x25 h2 y9e ff1 fs0 fc0 sc0 ls0 ws0">12.</div><div class="t m0 x45 h6 y9f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x72 h3 ya0 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x46 h3 ya1 ff2 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 xc1 h6 y9f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x47 h3 y9e ff2 fs0 fc0 sc0 ls1 ws0">=2</div><div class="t m0 x68 h5 ya2 ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff8">−<span class="ff5">1</span></span></div><div class="t m0 xf h4 ya3 ff4 fs0 fc0 sc0 ls0 ws0">−<span class="_ _8"> </span><span class="ff2">1<span class="ff3">,<span class="_ _1d"> </span><span class="ff1">13.</span></span></span></div><div class="t m0 x4d h6 ya4 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x79 h3 ya5 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x79 h3 ya6 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x7b h6 ya4 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x35 h3 ya3 ff2 fs0 fc0 sc0 ls0 ws0">=<span class="_ _7"> </span><span class="ff3">k</span></div><div class="t m0 x1a h6 ya4 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x63 h4 ya5 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1</span></span></div><div class="t m0 xb1 h3 ya6 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x53 h6 ya4 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x7c h3 ya3 ff2 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x7e h6 ya4 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xa6 h4 ya5 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1</span></span></div><div class="t m0 xa6 h4 ya6 ff3 fs0 fc0 sc0 ls0 ws0">k<span class="_ _7"> </span><span class="ff4">−<span class="_ _8"></span><span class="ff2">1</span></span></div><div class="t m0 x24 h6 ya4 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xa7 h3 ya3 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x8f h6 ya7 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x86 h5 ya8 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x86 h5 ya9 ff6 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x87 h6 ya7 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x6 h3 yaa ff2 fs0 fc0 sc0 ls0 ws0">Stirling<span class="_ _7"> </span>n<span class="_ _5"></span>um<span class="_ _5"></span>b<span class="_ _3"></span>ers<span class="_ _7"> </span>(2nd<span class="_ _8"> </span>kind):</div><div class="t m0 x6 h3 yab ff2 fs0 fc0 sc0 ls0 ws0">P<span class="_ _5"></span>artitions<span class="_ _11"> </span>of<span class="_ _11"> </span>an<span class="_ _11"> </span><span class="ff3">n<span class="_ _1e"> </span></span>elemen<span class="_ _5"></span>t</div><div class="t m0 x6 h3 y82 ff2 fs0 fc0 sc0 ls0 ws0">set in<span class="_ _5"></span>to <span class="ff3">k<span class="_ _0"> </span></span>non-empt<span class="_ _5"></span>y sets.</div><div class="t m0 x90 h6 yac ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x86 h5 yad ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x86 h5 yae ff6 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x87 h6 yac ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x6 h3 yaf ff2 fs0 fc0 sc0 ls0 ws0">1st order<span class="_ _0"> </span>Eulerian num<span class="_ _5"></span>bers:</div><div class="t m0 x6 h3 y8d ff2 fs0 fc0 sc0 ls0 ws0">P<span class="_ _5"></span>ermutations <span class="ff3">π</span></div><div class="t m0 xc2 h5 yb0 ff5 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m0 x4 h3 y8d ff3 fs0 fc0 sc0 ls0 ws0">π</div><div class="t m0 x1 h5 yb0 ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 xc3 h3 y8d ff3 fs0 fc0 sc0 ls7 ws0">...π</div><div class="t m0 xc4 h5 yb0 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x8 h3 y8d ff2 fs0 fc0 sc0 ls0 ws0">on</div><div class="t m0 x6 h4 y90 ff4 fs0 fc0 sc0 ls0 ws0">{<span class="ff2">1<span class="ff3">,<span class="_ _6"> </span></span>2<span class="ff3 ls4">,...,n<span class="_ _1f"></span><span class="ff4 ls0">}<span class="_ _0"> </span><span class="ff2">with<span class="_ _7"> </span><span class="ff3">k<span class="_ _0"> </span></span>ascen<span class="_ _5"></span>ts.</span></span></span></span></div><div class="t m0 x8f h6 yb1 ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _20"></span></div><div class="t m0 x86 h5 yb2 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x86 h5 yb3 ff6 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x87 h6 yb1 ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _20"></span></div><div class="t m0 x6 h3 yb4 ff2 fs0 fc0 sc0 ls0 ws0">2nd<span class="_ _8"> </span>order<span class="_ _7"> </span>Eulerian<span class="_ _8"> </span>num<span class="_ _5"></span>bers.</div><div class="t m0 xc5 h3 yb5 ff3 fs0 fc0 sc0 ls0 ws0">C</div><div class="t m0 xc6 h5 yb6 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x6 h3 yb5 ff2 fs0 fc0 sc0 ls0 ws0">Catalan<span class="_ _21"> </span>Num<span class="_ _5"></span>b<span class="_ _3"></span>ers:<span class="_ _22"> </span>Binary</div><div class="t m0 x6 h3 yb7 ff2 fs0 fc0 sc0 ls0 ws0">trees with <span class="ff3">n<span class="_ _8"> </span></span>+<span class="_ _8"> </span>1 v<span class="_ _5"></span>ertices.</div><div class="t m0 x3 h2 yb8 ff1 fs0 fc0 sc0 ls0 ws0">14.</div><div class="t m0 xc7 h6 yb9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x9a h3 yba ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xc5 h3 ybb ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 xc6 h6 yb9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xc8 h4 yb8 ff2 fs0 fc0 sc0 ls1 ws0">=(<span class="_ _b"></span><span class="ff3 ls0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1)!</span></span>,<span class="_ _23"> </span><span class="ff1">15.</span></span></div><div class="t m0 xc9 h6 yb9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x8e h3 yba ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x8e h3 ybb ff2 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 xca h6 yb9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xcb h4 yb8 ff2 fs0 fc0 sc0 ls1 ws0">=(<span class="_ _b"></span><span class="ff3 ls0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1)!</span></span>H</span></div><div class="t m0 x9b h5 ybc ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff8">−<span class="ff5">1</span></span></div><div class="t m0 x72 h3 yb8 ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _23"> </span><span class="ff1">16.</span></div><div class="t m0 xcc h6 yb9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xcd h3 yba ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xcd h3 ybb ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x16 h6 yb9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xce h3 yb8 ff2 fs0 fc0 sc0 ls1 ws0">=1<span class="_ _b"></span><span class="ff3 ls0">,<span class="_ _23"> </span><span class="ff1">17.</span></span></div><div class="t m0 xcf h6 yb9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xd0 h3 yba ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xd0 h3 ybb ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x1f h6 yb9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x55 h4 yb8 ff4 fs0 fc0 sc0 ls0 ws0">≥</div><div class="t m0 xd1 h6 yb9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xbf h3 yba ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xbf h3 ybb ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xd2 h6 yb9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xd3 h3 yb8 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x3 h2 ybd ff1 fs0 fc0 sc0 ls0 ws0">18.</div><div class="t m0 xc7 h6 ybe ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x9a h3 ybf ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xc5 h3 yc0 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xc6 h6 ybe ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xc8 h4 ybd ff2 fs0 fc0 sc0 ls1 ws0">=(<span class="_ _b"></span><span class="ff3 ls0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1)</span></span></span></div><div class="t m0 x2 h6 ybe ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x6 h4 ybf ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1</span></span></div><div class="t m0 x8b h3 yc0 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xd4 h6 ybe ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xd5 h3 ybd ff2 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 xd6 h6 ybe ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xd7 h4 ybf ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1</span></span></div><div class="t m0 xd7 h4 yc0 ff3 fs0 fc0 sc0 ls0 ws0">k<span class="_ _7"> </span><span class="ff4">−<span class="_ _8"></span><span class="ff2">1</span></span></div><div class="t m0 xd8 h6 ybe ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xd9 h3 ybd ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _24"> </span><span class="ff1">19.</span></div><div class="t m0 xda h6 ybe ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xdb h3 ybf ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xdc h4 yc0 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1</span></span></div><div class="t m0 x57 h6 ybe ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x9 h3 ybd ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x9c h6 ybe ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x9d h3 ybf ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x72 h4 yc0 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1</span></span></div><div class="t m0 x5b h6 ybe ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x68 h3 ybd ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x2c h6 ybe ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xf h3 ybf ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xf h3 yc0 ff2 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 x74 h6 ybe ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x75 h3 ybd ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _24"> </span><span class="ff1">20.</span></div><div class="t m0 x4a h5 yc1 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x3f h6 yc2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x3f h5 yc3 ff6 fs1 fc0 sc0 ls0 ws0">k<span class="ff5">=0</span></div><div class="t m0 x77 h6 yc4 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x4b h3 yc5 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x9f h3 yc6 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x30 h6 yc4 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xdd h3 yc7 ff2 fs0 fc0 sc0 ls0 ws0">=<span class="_ _7"> </span><span class="ff3">n</span>!<span class="ff3">,<span class="_ _24"> </span><span class="ff1">21.<span class="_ _1e"> </span></span>C</span></div><div class="t m0 xde h5 yc8 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x1d h3 yc9 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 xdf h3 yc5 ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 xbc h3 yca ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff2 ls2">+1</span></div><div class="t m0 x66 h6 ycb ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x7d h3 ycc ff2 fs0 fc0 sc0 ls0 ws0">2<span class="ff3">n</span></div><div class="t m0 xe0 h3 yca ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xd2 h6 ycb ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xd3 h3 yc9 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x3 h2 ycd ff1 fs0 fc0 sc0 ls0 ws0">22.</div><div class="t m0 xc7 h6 yce ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xe1 h3 ycf ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xe1 h3 yd0 ff2 fs0 fc0 sc0 ls0 ws0">0</div><div class="t m0 x87 h6 yce ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xe2 h3 ycd ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 xe3 h6 yce ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xe4 h3 ycf ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xe5 h4 yd0 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1</span></span></div><div class="t m0 x6 h6 yce ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xe6 h3 ycd ff2 fs0 fc0 sc0 ls1 ws0">=1<span class="_ _b"></span><span class="ff3 ls0">,<span class="_ _25"> </span><span class="ff1">23.</span></span></div><div class="t m0 xe7 h6 yce ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xc4 h3 ycf ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xc4 h3 yd0 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x7 h6 yce ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xe8 h3 ycd ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 xe9 h6 yce ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xea h3 ycf ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xeb h4 yd0 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1<span class="_ _8"> </span></span>−<span class="_ _8"> </span></span>k</div><div class="t m0 x73 h6 yce ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xd h3 ycd ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _25"> </span><span class="ff1">24.</span></div><div class="t m0 x13 h6 yce ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xcc h3 ycf ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xcc h3 yd0 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xcd h6 yce ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x6c h3 ycd ff2 fs0 fc0 sc0 ls1 ws0">=(<span class="_ _b"></span><span class="ff3 ls0">k<span class="_ _7"> </span><span class="ff2 ls2">+1<span class="_ _9"></span>)</span></span></div><div class="t m0 x43 h6 yce ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xec h4 ycf ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1</span></span></div><div class="t m0 x7b h3 yd0 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x4f h6 yce ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x6f h4 ycd ff2 fs0 fc0 sc0 ls2 ws0">+(<span class="_ _9"></span><span class="ff3 ls0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span></span>k<span class="_ _3"></span><span class="ff2">)</span></span></div><div class="t m0 xdf h6 yce ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x21 h4 ycf ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1</span></span></div><div class="t m0 x21 h4 yd0 ff3 fs0 fc0 sc0 ls0 ws0">k<span class="_ _7"> </span><span class="ff4">−<span class="_ _8"></span><span class="ff2">1</span></span></div><div class="t m0 xd2 h6 yce ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xd3 h3 ycd ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x3 h2 yd1 ff1 fs0 fc0 sc0 ls0 ws0">25.</div><div class="t m0 xc7 h6 yd2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xe1 h3 yd3 ff2 fs0 fc0 sc0 ls0 ws0">0</div><div class="t m0 xe1 h3 yd4 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x87 h6 yd2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xe2 h3 yd1 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 xe3 h6 yd5 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xe5 h3 yd6 ff2 fs0 fc0 sc0 ls5 ws0">1i<span class="_ _26"></span>f<span class="_ _27"></span><span class="ff3 ls0">k <span class="ff2 ls1">=0<span class="_ _b"></span>,</span></span></div><div class="t m0 xe5 h3 yd4 ff2 fs0 fc0 sc0 ls0 ws0">0<span class="_ _28"> </span>otherwise</div><div class="t m0 xed h2 yd1 ff1 fs0 fc0 sc0 ls0 ws0">26.</div><div class="t m0 xdc h6 yd2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xdb h3 yd3 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xdb h3 yd4 ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 xee h6 yd2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x26 h3 yd1 ff2 fs0 fc0 sc0 ls1 ws0">=2</div><div class="t m0 x28 h5 yd7 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 xef h4 yd8 ff4 fs0 fc0 sc0 ls0 ws0">−<span class="_ _8"> </span><span class="ff3">n<span class="_ _8"> </span></span>−<span class="_ _8"> </span><span class="ff2">1<span class="ff3">,<span class="_ _29"> </span><span class="ff1">27.</span></span></span></div><div class="t m0 x4b h6 yd9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x30 h3 yda ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x30 h3 ydb ff2 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 x17 h6 yd9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x43 h3 yd8 ff2 fs0 fc0 sc0 ls1 ws0">=3</div><div class="t m0 x4e h5 yd7 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x60 h4 yd8 ff4 fs0 fc0 sc0 ls0 ws0">−<span class="_ _8"> </span><span class="ff2">(<span class="ff3">n<span class="_ _8"> </span></span>+<span class="_ _8"> </span>1)2</span></div><div class="t m0 xcf h5 yd7 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x53 h3 yd8 ff2 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 xf0 h6 yd9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x65 h3 yda ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff2 ls2">+1</span></div><div class="t m0 x23 h3 ydb ff2 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 xd2 h6 yd9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xd3 h3 yd8 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x3 h3 ydc ff1 fs0 fc0 sc0 ls0 ws0">28.<span class="_ _1e"> </span><span class="ff3">x</span></div><div class="t m0 x9a h5 ydd ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 xc6 h3 yde ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x93 h5 ydf ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x88 h6 ye0 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x88 h5 ye1 ff6 fs1 fc0 sc0 ls0 ws0">k<span class="ff5">=0</span></div><div class="t m0 xf1 h6 ye2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xf2 h3 ye3 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xf2 h3 ye4 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xf3 h6 ye2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xf4 h3 ye3 ff3 fs0 fc0 sc0 ls0 ws0">x<span class="_ _8"> </span><span class="ff2">+<span class="_ _8"> </span></span>k</div><div class="t m0 xe6 h3 ye4 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xf5 h6 ye2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xd5 h3 yde ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _2a"> </span><span class="ff1">29.</span></div><div class="t m0 xc9 h6 ye2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xf6 h3 ye3 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xf7 h3 ye4 ff3 fs0 fc0 sc0 ls0 ws0">m</div><div class="t m0 xf8 h6 ye2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xda h3 yde ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 xe9 h5 ydf ff6 fs1 fc0 sc0 ls0 ws0">m</div><div class="t m0 xf9 h6 ye0 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xf9 h5 ye1 ff6 fs1 fc0 sc0 ls0 ws0">k<span class="ff5">=0</span></div><div class="t m0 xfa h6 ye2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x26 h3 ye3 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff2 ls2">+1</span></div><div class="t m0 x9 h3 ye4 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xef h6 ye2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x29 h4 yde ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff3">m<span class="_ _8"> </span></span><span class="ls2">+1</span><span class="ff4">−<span class="_ _8"> </span><span class="ff3">k<span class="_ _3"></span></span></span>)</div><div class="t m0 x74 h5 ydd ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x3c h4 yde ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff4">−</span>1)</div><div class="t m0 x13 h5 ydd ff6 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x5d h3 yde ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _2a"> </span><span class="ff1">30.<span class="_ _1e"> </span></span>m<span class="ff2">!</span></div><div class="t m0 x6d h6 ye5 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xfb h3 ye6 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xb6 h3 ye7 ff3 fs0 fc0 sc0 ls0 ws0">m</div><div class="t m0 x60 h6 ye5 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x4f h3 yde ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x19 h5 ydf ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x1a h6 ye0 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x1a h5 ye1 ff6 fs1 fc0 sc0 ls0 ws0">k<span class="ff5">=0</span></div><div class="t m0 x1c h6 ye2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x54 h3 ye3 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x54 h3 ye4 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xd0 h6 ye2 ff7 fs0 fc0 sc0 ls8 ws0"></div><div class="t m0 xd1 h3 ye3 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x55 h4 ye4 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span></span>m</div><div class="t m0 xd2 h6 ye2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xd3 h3 yde ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x3 h2 ye8 ff1 fs0 fc0 sc0 ls0 ws0">31.</div><div class="t m0 xc7 h6 ye9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x86 h3 yea ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 xe1 h3 yeb ff3 fs0 fc0 sc0 ls0 ws0">m</div><div class="t m0 xfc h6 ye9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x93 h3 ye8 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 xe5 h5 yec ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 xf1 h6 yed ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xf1 h5 yee ff6 fs1 fc0 sc0 ls0 ws0">k<span class="ff5">=0</span></div><div class="t m0 xf3 h6 yef ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x2 h3 yf0 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x2 h3 yf1 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xf4 h6 yef ff7 fs0 fc0 sc0 ls8 ws0"></div><div class="t m0 x8c h4 yf0 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span></span>k</div><div class="t m0 xd4 h3 yf1 ff3 fs0 fc0 sc0 ls0 ws0">m</div><div class="t m0 xfd h6 yef ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xd7 h4 yf2 ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff4">−</span>1)</div><div class="t m0 xc2 h5 yf3 ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff8">−</span>k<span class="ff8">−</span>m</div><div class="t m0 xfe h3 yf4 ff3 fs0 fc0 sc0 ls0 ws0">k<span class="_ _3"></span><span class="ff2">!</span>,<span class="_ _1c"> </span><span class="ff1">32.</span></div><div class="t m0 xff h6 yf5 ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _2b"></span></div><div class="t m0 x5c h3 yf6 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x5c h3 yf7 ff2 fs0 fc0 sc0 ls0 ws0">0</div><div class="t m0 x2d h6 yf5 ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _2b"></span></div><div class="t m0 x3c h3 yf4 ff2 fs0 fc0 sc0 ls1 ws0">=1<span class="_ _b"></span><span class="ff3 ls0">,<span class="_ _1c"> </span><span class="ff1">33.</span></span></div><div class="t m0 xa9 h6 yf5 ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _2b"></span></div><div class="t m0 x62 h3 yf6 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x62 h3 yf7 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x36 h6 yf5 ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _2b"></span></div><div class="t m0 x1c h4 yf4 ff2 fs0 fc0 sc0 ls0 ws0">=<span class="_ _7"> </span>0<span class="_ _28"> </span>for <span class="ff3">n<span class="_ _7"> </span><span class="ff4"></span></span><span class="ls1">=0<span class="_ _b"></span><span class="ff3 ls0">,</span></span></div><div class="t m0 x3 h2 yf8 ff1 fs0 fc0 sc0 ls0 ws0">34.</div><div class="t m0 xc7 h6 yf9 ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _2b"></span></div><div class="t m0 x86 h3 yfa ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x86 h3 yfb ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xfc h6 yf9 ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _2b"></span></div><div class="t m0 x100 h3 yf8 ff2 fs0 fc0 sc0 ls1 ws0">=(<span class="_ _b"></span><span class="ff3 ls0">k<span class="_ _7"> </span><span class="ff2 ls2">+1<span class="_ _9"></span>)</span></span></div><div class="t m0 x101 h6 yf9 ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _2b"></span></div><div class="t m0 x102 h4 yfa ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1</span></span></div><div class="t m0 x95 h3 yfb ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x103 h6 yf9 ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _2b"></span></div><div class="t m0 x104 h4 yf8 ff2 fs0 fc0 sc0 ls2 ws0">+(<span class="_ _9"></span>2<span class="_ _9"></span><span class="ff3 ls0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1<span class="_ _8"> </span></span>−<span class="_ _8"> </span></span>k<span class="_ _3"></span><span class="ff2">)</span></span></div><div class="t m0 x8 h6 yf9 ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _2b"></span></div><div class="t m0 xf9 h4 yfa ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1</span></span></div><div class="t m0 xf9 h4 yfb ff3 fs0 fc0 sc0 ls0 ws0">k<span class="_ _7"> </span><span class="ff4">−<span class="_ _8"></span><span class="ff2">1</span></span></div><div class="t m0 x26 h6 yf9 ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _2b"></span></div><div class="t m0 x9 h3 yf8 ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _2c"> </span><span class="ff1">35.</span></div><div class="t m0 x1b h5 yfc ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 xb8 h6 yfd ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xb8 h5 yfe ff6 fs1 fc0 sc0 ls0 ws0">k<span class="ff5">=0</span></div><div class="t m0 x52 h6 yff ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _2b"></span></div><div class="t m0 x54 h3 y100 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x54 h3 y101 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xd0 h6 yff ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _2b"></span></div><div class="t m0 x20 h3 y102 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x66 h3 yfa ff2 fs0 fc0 sc0 ls0 ws0">(2<span class="ff3">n</span>)</div><div class="t m0 x105 h5 y103 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 xa6 h3 y104 ff2 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 xbf h5 y105 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 xd3 h3 y106 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x3 h2 y107 ff1 fs0 fc0 sc0 ls0 ws0">36.</div><div class="t m0 xc7 h6 y108 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xfc h3 y109 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 xe1 h4 y10a ff3 fs0 fc0 sc0 ls0 ws0">x<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span></span>n</div><div class="t m0 x106 h6 y108 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x107 h3 y107 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x108 h5 y10b ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x109 h6 y10c ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x109 h5 y10d ff6 fs1 fc0 sc0 ls0 ws0">k<span class="ff5">=0</span></div><div class="t m0 x6 h6 y10e ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _2b"></span></div><div class="t m0 x10a h3 y10f ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x10a h3 y110 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x10b h6 y10e ff7 fs0 fc0 sc0 ls0 ws0"><span class="_ _2b"></span></div><div class="t m0 x10c h4 y10f ff3 fs0 fc0 sc0 ls0 ws0">x<span class="_ _8"> </span><span class="ff2">+<span class="_ _8"> </span></span>n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1<span class="_ _8"> </span></span>−<span class="_ _8"></span></span>k</div><div class="t m0 x10d h3 y110 ff2 fs0 fc0 sc0 ls0 ws0">2<span class="ff3">n</span></div><div class="t m0 xf7 h6 y10e ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xc4 h3 y111 ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _2d"> </span><span class="ff1">37.</span></div><div class="t m0 x2d h6 y10e ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xa8 h3 y10f ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff2 ls2">+1</span></div><div class="t m0 x10e h3 y110 ff3 fs0 fc0 sc0 ls0 ws0">m<span class="_ _8"> </span><span class="ff2 ls2">+1</span></div><div class="t m0 x14 h6 y10e ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x3e h3 y111 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x5e h6 y10c ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x76 h5 y10d ff6 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x10f h6 y10e ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x110 h3 y10f ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x110 h3 y110 ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x111 h6 y10e ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x6d h3 y10f ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x112 h3 y110 ff3 fs0 fc0 sc0 ls0 ws0">m</div><div class="t m0 xb6 h6 y10e ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x60 h3 y111 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x113 h5 y10b ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x4f h6 y10c ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x4f h5 y10d ff6 fs1 fc0 sc0 ls0 ws0">k<span class="ff5">=0</span></div><div class="t m0 x19 h6 y10e ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x1c h3 y10f ff3 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xbb h3 y110 ff3 fs0 fc0 sc0 ls0 ws0">m</div><div class="t m0 x54 h6 y10e ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xd0 h3 y111 ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff3">m<span class="_ _8"> </span></span><span class="ls2">+1<span class="_ _9"></span>)</span></div><div class="t m0 xe0 h5 y112 ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff8">−</span>k</div><div class="t m0 xd3 h3 y113 ff3 fs0 fc0 sc0 ls0 ws0">,</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div></div>