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A112164
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McKay-Thompson series of class 24g for the Monster group.
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3
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1, 3, -1, 3, -2, 9, 2, 9, -1, 24, 0, 27, 5, 51, -3, 60, -4, 108, 6, 129, -3, 210, -4, 252, 12, 393, -8, 474, -10, 702, 16, 852, -9, 1224, -8, 1485, 29, 2070, -17, 2511, -22, 3429, 38, 4155, -20, 5556, -20, 6723, 61, 8856, -36, 10695, -44, 13878, 80, 16722, -43, 21450, -44, 25785
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OFFSET
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0,2
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LINKS
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FORMULA
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Expansion of A + 3*q/A, where A = q^(1/2)*eta(q^2)*eta(q^4)/(eta(q^6) * eta(q^12)), in powers of q. - G. C. Greubel, Jun 25 2018
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EXAMPLE
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T24g = 1/q + 3*q - q^3 + 3*q^5 - 2*q^7 + 9*q^9 + 2*q^11 + 9*q^13 + ...
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MATHEMATICA
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eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^2]*eta[q^4]/( eta[q^6]*eta[q^12])); a:= CoefficientList[Series[A + 3*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 25 2018 *)
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PROG
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(PARI) q='q+O('q^60); A = eta(q^2)*eta(q^4)/(eta(q^6)*eta(q^12)); Vec(A + 3*q/A) \\ G. C. Greubel, Jun 25 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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STATUS
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approved
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