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A112174
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McKay-Thompson series of class 36d for the Monster group.
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1
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1, 1, 0, 2, -2, 0, 3, 1, 0, 4, 0, 0, 5, 0, 0, 8, -2, 0, 11, 4, 0, 16, -4, 0, 21, 4, 0, 26, -2, 0, 34, 1, 0, 44, -4, 0, 58, 9, 0, 74, -12, 0, 93, 9, 0, 116, -4, 0, 143, 5, 0, 178, -12, 0, 221, 20, 0, 272, -24, 0, 332, 20, 0, 402, -14, 0, 487, 13, 0, 588, -24, 0, 710, 42, 0, 854, -50, 0, 1021, 42, 0
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OFFSET
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0,4
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LINKS
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FORMULA
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Expansion of A + q/A, where A = q^(1/2)*(eta(q^6)*eta(q^9)/( eta(q^3)* eta(q^18)))^2, in powers of q. - G. C. Greubel, Jun 26 2018
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EXAMPLE
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T36d = 1/q +q +2*q^5 -2*q^7 +3*q^11 +q^13 +4*q^17 +5*q^23 +...
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MATHEMATICA
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eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^6]*eta[q^9]/( eta[q^3]*eta[q^18]))^2; a:= CoefficientList[Series[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 26 2018 *)
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PROG
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(PARI) q='q+O('q^80); A = (eta(q^6)*eta(q^9)/(eta(q^3)*eta(q^18)))^2; Vec(A+ q/A) \\ G. C. Greubel, Jun 26 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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