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A112177
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McKay-Thompson series of class 36h for the Monster group.
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1
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1, -2, 0, -1, -2, 0, 0, -2, 0, -2, -6, 0, 2, -6, 0, -1, -8, 0, 2, -14, 0, -2, -16, 0, 3, -20, 0, -4, -32, 0, 4, -38, 0, -4, -46, 0, 7, -66, 0, -7, -78, 0, 6, -96, 0, -10, -130, 0, 11, -154, 0, -11, -186, 0, 14, -244, 0, -16, -288, 0, 17, -346, 0, -21, -440, 0, 22, -518, 0, -24, -618, 0, 32, -768, 0, -34, -902, 0, 34, -1068
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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 - 2*q/A, where A = q^(1/2)*(eta(q^3)*eta(q^9)/(eta(q^6)* eta(q^18))), in powers of q. - G. C. Greubel, Jun 26 2018
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EXAMPLE
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T36h = 1/q -2*q -q^5 -2*q^7 -2*q^13 -2*q^17 -6*q^19 +2*q^23 +...
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MATHEMATICA
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eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^3]*eta[q^9]/( eta[q^6]*eta[q^18])); a:= CoefficientList[Series[A - 2*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^70); A = (eta(q^3)*eta(q^9)/(eta(q^6)* eta(q^18))); Vec(A - 2*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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