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A112147
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McKay-Thompson series of class 12A for the Monster group.
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2
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1, 0, 15, 32, 87, 192, 343, 672, 1290, 2176, 3705, 6336, 10214, 16320, 25905, 39936, 61227, 92928, 138160, 204576, 300756, 435328, 626727, 897408, 1271205, 1790592, 2508783, 3487424, 4824825, 6641664, 9083400, 12371904, 16778784
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OFFSET
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-1,3
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LINKS
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FORMULA
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Expansion of -6 + (eta(q^2)*eta(q^6))^12/((eta(q)*eta(q^3)*eta(q^4) *eta(q^12))^6) in powers of q. - G. C. Greubel, Jun 19 2018
a(n) ~ exp(2*Pi*sqrt(n/3)) / (2 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
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EXAMPLE
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T12A = 1/q + 15*q + 32*q^2 + 87*q^3 + 192*q^4 + 343*q^5 + 672*q^6 + ...
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MATHEMATICA
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eta[q_]:= q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[-6 + (eta[q^2]*eta[q^6])^12/((eta[q]*eta[q^3]*eta[q^4]*eta[q^12])^6), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = -6 + (eta(q^2)*eta(q^6))^12/((eta(q)*eta(q^3) *eta(q^4)*eta(q^12))^6)/q; Vec(A) \\ G. C. Greubel, Jun 19 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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STATUS
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approved
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