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A045486
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McKay-Thompson series of class 6C for Monster (and, apart from signs, of class 12A).
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3
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1, 2, 15, -32, 87, -192, 343, -672, 1290, -2176, 3705, -6336, 10214, -16320, 25905, -39936, 61227, -92928, 138160, -204576, 300756, -435328, 626727, -897408, 1271205, -1790592, 2508783, -3487424, 4824825, -6641664, 9083400, -12371904, 16778784, -22630912, 30407112, -40703040, 54238342, -72018624, 95300769
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OFFSET
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-1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) ~ (-1)^(n+1) * exp(2*Pi*sqrt(n/3)) / (2*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Apr 09 2016
Expansion of 8 + (eta(q)*eta(q^3)/(eta(q^2)*eta(q^6)))^6. - G. C. Greubel, Jun 02 2018
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MATHEMATICA
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nmax = 50; CoefficientList[Series[8*x + Product[((1-x^k)*(1-x^(3*k))/((1-x^(2*k))*(1-x^(6*k))))^6, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 09 2016 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[q*(8 + (eta[q]*eta[q^3]/(eta[q^2]*eta[q^6]))^6), {q, 0, 60}], q]; Table[ a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 02 2018 *)
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PROG
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(PARI) N=66; q='q+O('q^N); Vec( ((eta(q^1)*eta(q^3))/(eta(q^2)*eta(q^6)))^6/q + 8 ) \\ Joerg Arndt, Apr 09 2016
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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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