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%I #31 Jun 28 2018 17:33:31
%S 1,0,5,8,16,26,44,66,104,152,229,324,469,652,916,1250,1716,2306,3108,
%T 4116,5464,7156,9373,12144,15725,20190,25889,32952,41881,52904,66716,
%U 83688,104785,130608,162486,201336,249006,306874,377482,462860,566513,691404
%N McKay-Thompson series of class 21D for Monster.
%H Seiichi Manyama, <a href="/A058566/b058566.txt">Table of n, a(n) for n = -1..10000</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 -2 + (eta(q^3)*eta(q^7)/(eta(q)*eta(q^21)))^2 in powers of q. - _G. C. Greubel_, Jun 14 2018
%F a(n) ~ exp(4*Pi*sqrt(n/21)) / (sqrt(2) * 21^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018
%e T21D = 1/q + 5*q + 8*q^2 + 16*q^3 + 26*q^4 + 44*q^5 + 66*q^6 + 104*q^7 + ...
%t eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(-2 + (eta[q^3]*eta[q^7]/(eta[q]*eta[q^21]))^2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 14 2018 *)
%o (PARI) q='q+O('q^50); A = -2+(eta(q^3)*eta(q^7)/(eta(q)*eta(q^21)))^2/q; Vec(A) \\ _G. C. Greubel_, Jun 14 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%Y Cf. A226015 (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