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A058742
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McKay-Thompson series of class 68A for Monster.
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1
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1, 1, 1, 0, 2, 1, 3, 2, 4, 3, 6, 4, 7, 7, 10, 8, 14, 12, 18, 16, 23, 22, 30, 28, 39, 37, 49, 46, 62, 60, 78, 76, 97, 96, 122, 120, 150, 150, 185, 184, 228, 229, 278, 280, 338, 342, 410, 416, 495, 506, 597, 610, 718, 736, 859, 884, 1026, 1058, 1224, 1262, 1453, 1505, 1722, 1784, 2039
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OFFSET
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-1,5
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LINKS
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FORMULA
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a(n) ~ exp(2*Pi*sqrt(n/17)) / (2 * 17^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018
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EXAMPLE
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T68A = 1/q + q + q^3 + 2*q^7 + q^9 + 3*q^11 + 2*q^13 + 4*q^15 + 3*q^17 + ...
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MATHEMATICA
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QP := QPochhammer; nmax = 260; f[x_, y_] := QP[-x, x*y]*QP[-y, x*y]* QP[x*y, x*y]; G[x_] := f[-x^2, -x^3]/f[-x, -x^2]; H[x_] := f[-x, -x^4]/f[-x, -x^2]; A := G[x^34]*G[x] + x^7*H[x^34]*H[x]; B:= G[x^17]*H[x^2] - x^3*H[x^17]*G[x^2]; T34A := -2 + (A*B)^2/x; a:= CoefficientList[Series[(x*(2 + T34A) + O[x]^nmax)^(1/2), {x, 0, 100}], x]; Table[a[[n]], {n, 1, 80}] (* G. C. Greubel, Jun 29 2018 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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