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A045482
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McKay-Thompson series of class 5A for Monster.
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3
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1, 4, 134, 760, 3345, 12256, 39350, 114096, 307060, 776000, 1867170, 4298600, 9540169, 20487360, 42756520, 86967184, 172859325, 336450560, 642489660, 1205572920, 2226005750, 4049168800, 7264172196, 12864273920, 22507811570, 38936117376, 66640520250, 112915572144
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OFFSET
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-1,2
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LINKS
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FORMULA
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a(n) ~ exp(4*Pi*sqrt(n/5)) / (sqrt(2)*5^(1/4)*n^(3/4)). - Vaclav Kotesovec, Apr 01 2017
Expansion of 10 + F +125/F, where F = (eta(q)/eta(q^5))^6, in powers of q. - G. C. Greubel, Jun 02 2018
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MATHEMATICA
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nmax = 30; CoefficientList[Series[10*x + 125*x^2*Product[((1 - x^(5*k))/(1 - x^k))^6, {k, 1, nmax}] + Product[((1 - x^k)/(1 - x^(5*k)))^6, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 01 2017 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[ q*(10 + (eta[q]/eta[q^5])^6 + 125*(eta[q^5]/eta[q])^6), {q, 0, 60}], q];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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