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A058097
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McKay-Thompson series of class 10A for Monster.
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2
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1, 0, 22, 56, 177, 352, 870, 1584, 3412, 5952, 11442, 19240, 34377, 56256, 95560, 151824, 247965, 385024, 609756, 927864, 1431094, 2139680, 3228516, 4752896, 7038610, 10215552, 14885450, 21330480, 30643161, 43407680, 61571148, 86305680, 121034807, 168032768
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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(2*n/5)) / (2^(3/4)*5^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 30 2017
Expansion of A - 6 + 1/A, where A = (eta(q^2)*eta(q^5)/(eta(q)*eta(q^10) ))^6, in powers of q. - G. C. Greubel, Jun 13 2018
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EXAMPLE
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T10A = 1/q + 22*q + 56*q^2 + 177*q^3 + 352*q^4 + 870*q^5 + 1584*q^6 + ...
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MATHEMATICA
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nmax = 50; CoefficientList[Series[(4*x*Product[((1 + x^k)*(1 + x^(5*k)))^2, {k, 1, nmax}] + Product[(1/(1 + x^(5*k))/(1 + x^k))^2, {k, 1, nmax}])^2 - 4*x, {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 30 2017 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(-6 + (eta[q^2]*eta[q^5]/(eta[q]*eta[q^10]))^6 + (eta[q]*eta[q^10]/( eta[q^2]*eta[q^5]))^6), {q, 0, 60}, Assumptions->q>0], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 13 2018 *)
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PROG
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(PARI) q='q+O('q^30); A = (eta(q^2)*eta(q^5)/(eta(q)*eta(q^10)))^6/q; Vec(A - 6 + 1/A) \\ G. C. Greubel, Jun 13 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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