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A058725
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McKay-Thompson series of class 60A for the Monster group.
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1
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1, 2, 0, 1, 1, 3, 1, 6, 3, 5, 7, 9, 8, 14, 9, 17, 18, 24, 21, 33, 30, 40, 43, 54, 52, 77, 69, 93, 97, 117, 121, 160, 153, 191, 200, 246, 250, 319, 312, 381, 410, 480, 494, 607, 609, 733, 775, 903, 937, 1120, 1152, 1345, 1431, 1638, 1712, 2020, 2085, 2406
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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 + q/A, where A = q^(1/2)*(eta(q^2)*eta(q^3)*eta(q^10) *eta(q^15)/(eta(q)*eta(q^5)*eta(q^6)*eta(q^30))), in powers of q. - G. C. Greubel, Jun 28 2018
a(n) ~ exp(2*Pi*sqrt(n/15)) / (2 * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
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EXAMPLE
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T60A = 1/q + 2*q + q^5 + q^7 + 3*q^9 + q^11 + 6*q^13 + 3*q^15 + 5*q^17 + ...
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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^3]* eta[q^10]*eta[q^15]/(eta[q]*eta[q^5]*eta[q^6]*eta[q^30])); a:= SeriesCoefficient[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 28 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^3)*eta(q^10)*eta(q^15)/(eta(q)* eta(q^5)*eta(q^6)*eta(q^30))); Vec(A + q/A) \\ G. C. Greubel, Jun 28 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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