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A058648
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McKay-Thompson series of class 36a for Monster.
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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
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OFFSET
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-1,4
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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 23 2018
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EXAMPLE
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T36a = 1/q - q + 2*q^5 + 2*q^7 + 3*q^11 - q^13 + 4*q^17 + 5*q^23 + 8*q^29 + ...
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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 23 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = (eta(q^6)*eta(q^9)/(eta(q^3)*eta(q^18)))^2; Vec(A - q/A) \\ G. C. Greubel, Jun 23 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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