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A058768
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McKay-Thompson series of class 94A for the Monster group.
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1
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1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 4, 3, 5, 4, 6, 5, 8, 6, 9, 8, 12, 10, 14, 12, 17, 15, 20, 18, 25, 22, 29, 27, 35, 32, 41, 38, 49, 46, 57, 54, 68, 64, 79, 76, 93, 89, 108, 104, 126, 122, 146, 142, 170, 165, 195, 192, 226, 222, 260, 256, 299, 296, 342
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OFFSET
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-1,9
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COMMENTS
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Also McKay-Thompson series of class 94B for Monster. - Michel Marcus, Feb 24 2014
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LINKS
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FORMULA
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a(n) ~ exp(4*Pi*sqrt(n/94)) / (sqrt(2) * 94^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 10 2018
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EXAMPLE
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T94A = 1/q + q + q^3 + q^4 + q^5 + q^6 + 2*q^7 + q^8 + 2*q^9 + 2*q^10 + 3*q^11 + ...
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MATHEMATICA
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eta[q_] := q^(1/24)*QPochhammer[q]; Theta[a_, b_, c_] := Sum[q^((a*n^2 + b*n*m + c*m^2)/2), {n, -50, 50}, {m, -50, 50}]; T47A:= (Theta[2, 2, 24] - Theta[4, 2, 12])/(2*eta[q]*eta[q^47]); a:= CoefficientList[Series[ q*(T47A + (T47A /. {q -> q^2}) + T47A*(T47A /. {q -> q^2}))/(1 + T47A + (T47A /. {q -> q^2})), {q, 0, 100}], q]; Table[a[[n]], {n, 1, 75}] (* G. C. Greubel, Jul 25 2018 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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