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A058538
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McKay-Thompson series of class 18c for Monster.
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1
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1, 3, 9, 16, 33, 54, 98, 150, 243, 364, 564, 828, 1221, 1749, 2511, 3528, 4938, 6804, 9358, 12714, 17217, 23068, 30822, 40824, 53916, 70659, 92340, 119912, 155277, 199980, 256792, 328218, 418311, 530960, 672072, 847584, 1066157, 1336686, 1671741, 2084464, 2593059, 3216834, 3981926
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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 q^(1/2)*(eta(q^3)^2/(eta(q)*eta(q^9)))^3 in powers of q. - G. C. Greubel, Jun 20 2018
a(n) ~ exp(2*Pi*sqrt(2*n)/3) / (2^(3/4) * sqrt(3) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
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EXAMPLE
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T18c = 1/q + 3*q + 9*q^3 + 16*q^5 + 33*q^7 + 54*q^9 + 98*q^11 + 150*q^13 + ...
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MATHEMATICA
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eta[q_] := q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[q^(1/2)*(eta[q^3]^2/(eta[q]*eta[q^9]))^3, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 20 2018 *)
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PROG
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(PARI) q='q+O('q^50); Vec((eta(q^3)^2/(eta(q)*eta(q^9)))^3) \\ G. C. Greubel, Jun 20 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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