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A058708
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McKay-Thompson series of class 54A for the Monster group.
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1
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1, 0, 1, 1, 3, 2, 4, 3, 6, 5, 9, 8, 14, 12, 19, 18, 27, 26, 37, 36, 52, 50, 69, 68, 93, 93, 122, 124, 162, 164, 210, 216, 274, 281, 351, 364, 451, 468, 572, 598, 726, 760, 913, 960, 1148, 1208, 1431, 1512, 1782, 1884, 2206, 2339, 2727, 2892, 3353, 3564, 4114
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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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Expansion of -1 + A*B/x in powers of q, where A = G(x^54)*G(x) + x^11* H(x^54)*H(x), B = G(x^27)*H(x^2) - x^5*H(x^27)*G(x^2), G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jun 29 2018
a(n) ~ exp(2*Pi*sqrt(2*n/3)/3) / (6^(3/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018
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EXAMPLE
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T54A = 1/q + q + q^2 + 3*q^3 + 2*q^4 + 4*q^5 + 3*q^6 + 6*q^7 + 5*q^8 + 9*q^9 + ...
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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^54]*G[x^1] + x^11*H[x^54]*H[x^1]; B:= G[x^27]*H[x^2] - x^5*H[x^27]*G[x^2]; a:= CoefficientList[Series[-x + 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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