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A058726
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McKay-Thompson series of class 60B for Monster.
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2
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1, 0, 0, 2, 2, 2, 3, 2, 5, 6, 5, 6, 9, 10, 10, 16, 17, 18, 25, 26, 31, 38, 37, 48, 60, 62, 68, 84, 95, 104, 125, 134, 154, 182, 192, 220, 257, 274, 309, 360, 394, 434, 492, 544, 607, 688, 740, 824, 944, 1018, 1123, 1266, 1377, 1524, 1697, 1850, 2041, 2264
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OFFSET
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-1,4
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LINKS
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FORMULA
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a(n) ~ exp(2*Pi*sqrt(n/15)) / (2*15^(1/4)*n^(3/4)). - Vaclav Kotesovec, Jun 06 2018
Expansion of -1 + (eta(q^2)*eta(q^6)*eta(q^10)*eta(q^30))^2/(eta(q)* eta(q^3)*eta(q^4)*eta(q^5)*eta(q^12)*eta(q^15)*eta(q^20)*eta(q^60)) in powers of q. - G. C. Greubel, Jun 28 2018
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EXAMPLE
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T60B = 1/q + 2*q^2 + 2*q^3 + 2*q^4 + 3*q^5 + 2*q^6 + 5*q^7 + 6*q^8 + 5*q^9 + ...
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MATHEMATICA
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nmax = 60; CoefficientList[Series[-x + 1/Product[(1 + x^(2*k))*(1 + x^(6*k))*(1 + x^(10*k))*(1 + x^(30*k))*(1 - x^(2*k - 1))*(1 - x^(6*k - 3))*(1 - x^(10*k - 5))*(1 - x^(30*k - 15)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 06 2018 *)
eta[q_] := q^(1/24)*QPochhammer[q]; A:= (eta[q^2]*eta[q^6]*eta[q^10]* eta[q^30])^2/(eta[q]*eta[q^3]*eta[q^4]*eta[q^5]*eta[q^12]*eta[q^15]* eta[q^20]*eta[q^60]); a:= CoefficientList[Series[-1 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 28 2018 *)
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PROG
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(PARI) q='q+O('q^50); A = -1 + (eta(q^2)*eta(q^6)*eta(q^10)* eta(q^30))^2/(eta(q)*eta(q^3)*eta(q^4)*eta(q^5)*eta(q^12)*eta(q^15) *eta(q^20) *eta(q^60))/q; Vec(A) \\ G. C. Greubel, Jun 28 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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