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A058557
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McKay-Thompson series of class 20b for Monster.
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1
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1, 4, 3, 16, 20, 48, 55, 108, 141, 248, 326, 516, 662, 1048, 1335, 2000, 2547, 3672, 4689, 6588, 8379, 11500, 14513, 19644, 24688, 32896, 41115, 53964, 67301, 87312, 108385, 139124, 171876, 218852, 269284, 339996, 416665, 522104, 637698, 793704, 965989, 1194888, 1448933, 1782800
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OFFSET
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-1,2
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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^2)*eta(q^5)/(eta(q)* eta(q^10)))^3, in powers of q. - G. C. Greubel, Jun 21 2018
a(n) ~ exp(2*Pi*sqrt(n/5)) / (2 * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
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EXAMPLE
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T20b = 1/q + 4*q + 3*q^3 + 16*q^5 + 20*q^7 + 48*q^9 + 55*q^11 + 108*q^13 + ...
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MATHEMATICA
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eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]*eta[q^5]/(eta[q]*eta[q^10]))^3; a:= CoefficientList[Series[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^5)/(eta(q)* eta(q^10)))^3; Vec(A + q/A) \\ G. C. Greubel, Jun 21 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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