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%I #19 Jun 19 2018 12:32:12
%S 1,0,3,4,7,10,17,22,32,44,62,80,112,144,193,248,323,410,530,664,845,
%T 1054,1324,1634,2037,2498,3082,3760,4601,5580,6789,8186,9891,11876,
%U 14271,17052,20393,24260,28876,34224,40557,47888,56540,66516,78240
%N McKay-Thompson series of class 29A for Monster.
%H G. C. Greubel, <a href="/A058611/b058611.txt">Table of n, a(n) for n = -1..1000</a>
%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 <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/29)) / (sqrt(2)*29^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Sep 07 2017
%F G.f.: - 2 + x^(-1) * ( G(x) * G(x^29) + x^6 * H(x) * H(x^29) )^2 where G() is g.f. of A003114 and H() is g.f. of A003106. - _G. C. Greubel_, Jun 18 2018
%e T29A = 1/q + 3*q + 4*q^2 + 7*q^3 + 10*q^4 + 17*q^5 + 22*q^6 + 32*q^7 + ...
%t eta[q_]:= q^(1/24)*QPochhammer[q]; e26B := ((eta[q^2]*eta[q^13])/(eta[q] *eta[q^26]))^2; G[q_] := QPochhammer[q^2, q^5]*QPochhammer[q^3, q^5]* QPochhammer[q^5]/QPochhammer[q]; H[q_] := QPochhammer[q, q^5]* QPochhammer[q^4, q^5]*QPochhammer[q^5]/QPochhammer[q]; a:= CoefficientList[Series[q*(-2 + (1/q)*(G[q]*G[q^29] + q^6*H[q]*H[q^29])^2 ), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 18 2018 *)
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%Y Cf. A136570 (same sequence except for n=0).
%K nonn
%O -1,3
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Michel Marcus_, Feb 18 2014
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