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A058704
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McKay-Thompson series of class 51A for the Monster group.
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2
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1, 0, 1, 2, 2, 2, 5, 4, 6, 8, 9, 10, 17, 16, 19, 26, 29, 34, 46, 48, 59, 72, 80, 92, 117, 126, 148, 178, 198, 226, 274, 298, 345, 404, 450, 510, 601, 660, 753, 866, 965, 1084, 1253, 1378, 1558, 1770, 1965, 2196, 2501, 2752, 3085, 3476, 3845, 4276, 4820, 5298
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OFFSET
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-1,4
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LINKS
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FORMULA
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Expansion of A*B in powers of q, where A = G(q^17)*G(q^3) + q^4*H(q^17) *H(q^3), B = G(q^51)*H(q) - q^10*H(q^51)*G(q), G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jun 29 2018
a(n) ~ exp(4*Pi*sqrt(n/51)) / (sqrt(2) * 51^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018
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EXAMPLE
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T51A = 1/q + q + 2*q^2 + 2*q^3 + 2*q^4 + 5*q^5 + 4*q^6 + 6*q^7 + 8*q^8 + ...
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MATHEMATICA
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QP := QPochhammer; 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^17]*G[x^3] + x^4*H[x^17]*H[x^3]; B := G[x^51]*H[x] - x^10*H[x^51]*G[x]; a := CoefficientList[Series[A*B, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* 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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