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A112180
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McKay-Thompson series of class 40a for the Monster group.
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1
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1, 0, 3, 4, 4, 4, 7, 12, 13, 16, 22, 28, 38, 44, 55, 72, 83, 104, 129, 156, 187, 220, 273, 328, 384, 452, 539, 652, 757, 880, 1041, 1220, 1428, 1652, 1924, 2244, 2585, 2992, 3458, 3992, 4581, 5244, 6053, 6936, 7910, 9024, 10303, 11784, 13380, 15176
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OFFSET
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0,3
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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^4)*eta(q^5)/( eta(q)* eta(q^20))), in powers of q. - G. C. Greubel, Jun 26 2018
a(n) ~ exp(Pi*sqrt(2*n/5)) / (2^(5/4) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 27 2018
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EXAMPLE
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T40a = 1/q +3*q^3 +4*q^5 +4*q^7 +4*q^9 +7*q^11 +12*q^13 +...
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MATHEMATICA
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eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^4]*eta[q^5]/( eta[q]*eta[q^20])); a := CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 26 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = eta(q^4)*eta(q^5)/(eta(q)*eta(q^20)); Vec(A - q/A) \\ G. C. Greubel, Jun 26 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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