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%I #21 Jun 28 2018 04:27:38
%S 1,3,6,13,24,39,64,102,153,230,342,492,704,999,1392,1922,2637,3576,
%T 4812,6438,8547,11278,14802,19317,25078,32403,41670,53358,68043,86424,
%U 109378,137934,173346,217166,271218,337692,419287,519174,641124,789744,970455,1189659,1455086,1775850
%N McKay-Thompson series of class 20E for Monster.
%H G. C. Greubel, <a href="/A058554/b058554.txt">Table of n, a(n) for n = -1..2500</a>
%H D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Comm. 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 q^(1/2)*(eta(q^2)*eta(q^5)/(eta(q)*eta(q^10)))^3 in powers of q. - _G. C. Greubel_, Jun 21 2018
%F a(n) ~ exp(2*Pi*sqrt(n/5)) / (2 * 5^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018
%e T20E = 1/q + 3*q + 6*q^3 + 13*q^5 + 24*q^7 + 39*q^9 + 64*q^11 + 102*q^13 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[q^(1/2)*(eta[q^2]*eta[q^5]/(eta[q]*eta[q^10]))^3, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 21 2018 *)
%o (PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^5)/(eta(q)*eta(q^10)))^3; Vec(A) \\ _G. C. Greubel_, Jun 21 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,2
%A _N. J. A. Sloane_, Nov 27 2000
%E Terms a(12) onward added by _G. C. Greubel_, Jun 21 2018
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