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A112198
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McKay-Thompson series of class 56c for the Monster group.
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1
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1, -1, 1, 1, 1, 0, 2, 1, 2, -1, 3, 1, 4, -1, 4, 0, 5, -1, 7, 2, 8, -1, 10, 1, 12, -2, 14, 2, 17, -3, 21, 3, 24, -3, 28, 4, 34, -4, 39, 4, 46, -5, 53, 4, 61, -4, 71, 6, 82, -6, 94, 7, 108, -7, 124, 8, 142, -11, 162, 11, 185, -10, 210, 12, 238, -14, 271, 15, 306, -15, 345, 14, 390, -17, 439, 20, 494
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OFFSET
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0,7
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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^14)/(eta(q^2)* eta(q^28))), in powers of q. - G. C. Greubel, Jul 01 2018
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EXAMPLE
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T56c = 1/q - q + q^3 + q^5 + q^7 + 2*q^11 + q^13 + 2*q^15 - q^17 + ...
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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^14]/(eta[q^2]*eta[q^28])); a:= CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 01 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = eta(q^4)*eta(q^14)/(eta(q^2)*eta(q^28)); Vec(A - q/A) \\ G. C. Greubel, Jul 01 2018
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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