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A058714
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McKay-Thompson series of class 56A for the Monster group.
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1
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1, 0, 1, 2, 1, 2, 3, 4, 5, 6, 8, 8, 10, 12, 15, 18, 22, 26, 29, 34, 39, 48, 55, 64, 76, 84, 97, 112, 128, 146, 168, 192, 217, 246, 277, 316, 355, 402, 454, 508, 572, 640, 721, 804, 898, 1008, 1119, 1248, 1392, 1548, 1718, 1910, 2118, 2344, 2598, 2872, 3181
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OFFSET
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-1,4
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LINKS
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FORMULA
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Expansion of -1 + eta(q^2)*eta(q^4)*eta(q^14)*eta(q^28)/(eta(q)*eta(q^7) *eta(q^8)*eta(q^56)) in powers of q. - G. C. Greubel, Jun 27 2018
a(n) ~ exp(sqrt(2*n/7)*Pi) / (2^(5/4) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
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EXAMPLE
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T56A = 1/q + q + 2*q^2 + q^3 + 2*q^4 + 3*q^5 + 4*q^6 + 5*q^7 + 6*q^8 + 8*q^9 + ...
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MATHEMATICA
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eta[q_] := q^(1/24)*QPochhammer[q]; A := (eta[q^2]*eta[q^4]*eta[q^14]* eta[q^28]/(eta[q]*eta[q^7]*eta[q^8]*eta[q^56])); a:= CoefficientList[ Series[-1 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 27 2018 *)
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PROG
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(PARI) q='q+O('q^50); Vec(-1 + eta(q^2)*eta(q^4)*eta(q^14)*eta(q^28)/(q* eta(q)*eta(q^7)*eta(q^8)*eta(q^56))) \\ G. C. Greubel, Jun 27 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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