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%I #25 Jun 26 2018 08:42:48
%S 1,0,2,2,4,5,7,9,13,16,22,27,36,43,56,68,87,104,130,156,193,230,281,
%T 333,404,477,572,673,802,940,1113,1299,1531,1780,2085,2418,2820,3259,
%U 3784,4362,5047,5799,6685,7662,8806,10066,11532,13152,15026,17098,19482
%N McKay-Thompson series of class 39C for Monster.
%C Also McKay-Thompson series of class 39D for Monster. - _Michel Marcus_, Feb 19 2014
%H G. C. Greubel, <a href="/A058661/b058661.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 Expansion of -1 + (eta(q^3)*eta(q^13))/(eta(q)*eta(q^39)) in powers of q. - _G. C. Greubel_, Jun 19 2018
%F a(n) ~ exp(4*Pi*sqrt(n/39)) / (sqrt(2) * 39^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 26 2018
%e T39C = 1/q + 2*q + 2*q^2 + 4*q^3 + 5*q^4 + 7*q^5 + 9*q^6 + 13*q^7 + 16*q^8 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*((eta[q^3]*eta[q^13])/(eta[q]*eta[q^39]) - 1), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 19 2018*)
%o (PARI) q='q+O('q^50); Vec((eta(q^3)*eta(q^13))/(q*eta(q)*eta(q^39)) - 1) \\ _G. C. Greubel_, Jun 19 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%Y Cf. A094362 (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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