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A058736
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McKay-Thompson series of class 62A for Monster.
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1
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1, 0, 1, 1, 2, 1, 3, 2, 5, 4, 6, 5, 9, 8, 12, 11, 17, 15, 23, 21, 31, 29, 39, 38, 53, 50, 67, 66, 87, 85, 111, 110, 141, 141, 177, 178, 223, 225, 277, 283, 346, 352, 427, 438, 527, 542, 645, 666, 792, 818, 962, 1000, 1170, 1216, 1416, 1476, 1711, 1786, 2057
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OFFSET
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-1,5
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COMMENTS
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Also McKay-Thompson series of class 62B for Monster. - Michel Marcus, Feb 24 2014
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LINKS
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FORMULA
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Expansion of (T31A(q) * T31A(q^2))^(1/3) in powers of q, where T31A(q) = A058628. - G. C. Greubel, Jun 29 2018
a(n) ~ exp(2*Pi*sqrt(2*n/31)) / (2^(3/4) * 31^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018
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EXAMPLE
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T62A = 1/q + q + q^2 + 2*q^3 + q^4 + 3*q^5 + 2*q^6 + 5*q^7 + 4*q^8 + 6*q^9 + ...
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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]; B3 := ( G[x^31]*H[x] - x^6*H[x^31]*G[x])^3; a:= CoefficientList[Series[(B3 * (B3 /. {x -> x^2}) + O[x]^nmax)^(1/3), {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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