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A058546
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McKay-Thompson series of class 18h for Monster.
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1
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1, 0, 4, -2, 0, 8, 1, 0, 12, -4, 0, 32, 8, 0, 52, -6, 0, 80, 10, 0, 148, -16, 0, 224, 18, 0, 332, -26, 0, 536, 33, 0, 784, -40, 0, 1120, 58, 0, 1676, -74, 0, 2368, 82, 0, 3296, -112, 0, 4704, 147, 0, 6472, -166, 0, 8808, 212, 0, 12160, -268, 0, 16384, 316, 0, 21884, -392, 0, 29472, 476
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OFFSET
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-1,3
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LINKS
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FORMULA
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Expansion of A + 4*q^2/A, where A = q*(eta(q^3)*eta(q^9)/(eta(q^6) *eta(q^18)))^2, in powers of q. - G. C. Greubel, Jun 21 2018
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EXAMPLE
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T18h = 1/q + 4*q - 2*q^2 + 8*q^4 + q^5 + 12*q^7 - 4*q^8 + 32*q^10 + 8*q^11 + ...
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MATHEMATICA
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eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q*(eta[q^3]*eta[q^9]/(eta[q^6] *eta[q^18]))^2; a:= CoefficientList[Series[A + 4*q^2/A, {q, 0, 80}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *)
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PROG
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(PARI) q='q+O('q^60); A = (eta(q^3)*eta(q^9)/(eta(q^6)*eta(q^18)))^2; Vec(A + 4*q^2/A) \\ G. C. Greubel, Jun 21 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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EXTENSIONS
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STATUS
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approved
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