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A112156
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McKay-Thompson series of class 18g for the Monster group.
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1
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1, 3, 0, -2, 6, 0, -1, 15, 0, 4, 24, 0, -3, 48, 0, 0, 78, 0, 7, 132, 0, -8, 204, 0, -3, 324, 0, 14, 486, 0, -14, 735, 0, -4, 1068, 0, 26, 1563, 0, -26, 2220, 0, -7, 3159, 0, 44, 4404, 0, -41, 6135, 0, -10, 8412, 0, 73, 11508, 0, -72, 15552, 0, -20, 20964, 0, 118, 27978, 0, -109
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OFFSET
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0,2
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LINKS
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FORMULA
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Expansion of A + 3*q/A, where A = q^(1/2)*(eta(q^3)/eta(q^9))^2, in powers of q. - G. C. Greubel, Jun 25 2018
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EXAMPLE
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T18g = 1/q + 3*q - 2*q^5 + 6*q^7 - q^11 + 15*q^13 + 4*q^17 + 24*q^19 + ...
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MATHEMATICA
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eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^3]/eta[q^9])^2; a:= CoefficientList[Series[A + 3*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 25 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = (eta(q^3)/eta(q^9))^2; Vec(A + 3*q/A) \\ G. C. Greubel, Jun 25 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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