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%I #24 Jun 02 2018 21:27:32
%S 1,4,134,760,3345,12256,39350,114096,307060,776000,1867170,4298600,
%T 9540169,20487360,42756520,86967184,172859325,336450560,642489660,
%U 1205572920,2226005750,4049168800,7264172196,12864273920,22507811570,38936117376,66640520250,112915572144
%N McKay-Thompson series of class 5A for Monster.
%H Vincenzo Librandi, <a href="/A045482/b045482.txt">Table of n, a(n) for n = -1..1000</a>
%H J. H. Conway and S. P. Norton, <a href="http://blms.oxfordjournals.org/content/11/3/308.extract">Monstrous Moonshine</a>, Bull. Lond. Math. Soc. 11 (1979) 308-339.
%H D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Commun. Algebra 22, No. 13, 5175-5193 (1994).
%H J. McKay and H. Strauss, <a href="http://dx.doi.org/10.1080/00927879008823911">The q-series of monstrous moonshine and the decomposition of the head characters</a>, Comm. Algebra 18 (1990), no. 1, 253-278.
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F a(n) ~ exp(4*Pi*sqrt(n/5)) / (sqrt(2)*5^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Apr 01 2017
%F Expansion of 10 + F +125/F, where F = (eta(q)/eta(q^5))^6, in powers of q. - _G. C. Greubel_, Jun 02 2018
%t 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 *)
%t 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];
%t Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 02 2018 *)
%Y Cf. A007251.
%K nonn
%O -1,2
%A _N. J. A. Sloane_
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