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A058553
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McKay-Thompson series of class 20D for Monster.
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1
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1, -2, 1, -2, 4, -6, 9, -8, 13, -20, 22, -28, 34, -46, 57, -68, 87, -104, 127, -152, 187, -232, 267, -318, 388, -462, 545, -632, 753, -896, 1043, -1216, 1416, -1664, 1928, -2228, 2597, -2996, 3454, -3976, 4585, -5286, 6031, -6900, 7918, -9060, 10325, -11720, 13372, -15228, 17259, -19564
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listen;
history;
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OFFSET
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-1,2
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LINKS
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FORMULA
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Expansion of q^(1/2)*(eta(q)*eta(q^5)/(eta(q^2)*eta(q^10)))^2 in powers of q. - G. C. Greubel, Jun 21 2018
a(n) ~ -(-1)^n * exp(sqrt(2*n/5)*Pi) / (2^(5/4) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
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EXAMPLE
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T20D = 1/q - 2*q + q^3 - 2*q^5 + 4*q^7 - 6*q^9 + 9*q^11 - 8*q^13 + 13*q^15 - ...
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MATHEMATICA
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eta[q_] := q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[q^(1/2)*(eta[q]*eta[q^5]/(eta[q^2]*eta[q^10]))^2, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *)
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PROG
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(PARI) q='q+O('q^60); A = (eta(q)*eta(q^5)/(eta(q^2)*eta(q^10)))^2; Vec(A) \\ G. C. Greubel, Jun 21 2018
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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