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A058555
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McKay-Thompson series of class 20F for Monster.
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3
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1, 0, 5, 10, 18, 30, 51, 80, 124, 190, 281, 410, 592, 840, 1178, 1640, 2253, 3070, 4154, 5570, 7422, 9830, 12932, 16920, 22028, 28520, 36761, 47180, 60280, 76720, 97278, 122880, 154693, 194110, 242776, 302740, 376424, 466710, 577114, 711800, 875707, 1074790
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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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a(n) ~ exp(2*Pi*sqrt(n/5)) / (2*5^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 21 2018
Expansion of -2 + (eta(q^4)*eta(q^5)/(eta(q)*eta(q^20)))^2 in powers of q. - G. C. Greubel, Jun 14 2018
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EXAMPLE
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T20F = 1/q + 5*q + 10*q^2 + 18*q^3 + 30*q^4 + 51*q^5 + 80*q^6 + 124*q^7 + ...
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MATHEMATICA
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nmax = 50; QP=QPochhammer; CoefficientList[Series[-2*x + (QP[x^4] *QP[x^5]/(QP[x]*QP[x^20]))^2, {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 21 2018 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(-2 + (eta[q^4]*eta[q^5]/(eta[q]*eta[q^20]))^2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 14 2018 *)
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PROG
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(PARI) q='q+O('q^50); A= -2 + (eta(q^4)*eta(q^5)/(eta(q)*eta(q^20)))^2/q; Vec(A) \\ G. C. Greubel, Jun 14 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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