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%I #20 Jun 28 2018 04:37:03
%S 1,4,10,24,47,84,150,248,403,648,1002,1536,2316,3420,5004,7224,10309,
%T 14592,20456,28440,39240,53736,73102,98808,132779,177444,235868,
%U 312024,410785,538368,702630,913208,1182342,1525200,1960418,2511360,3206675,4081576,5179670,6554112,8270086
%N McKay-Thompson series of class 16A for Monster.
%H G. C. Greubel, <a href="/A058514/b058514.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>, 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^4)/(eta(q)*eta(q^8)))^4 in powers of q. - _G. C. Greubel_, Jun 20 2018
%F a(n) ~ exp(sqrt(n)*Pi) / (2^(3/2) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018
%e T16A = 1/q + 4*q + 10*q^3 + 24*q^5 + 47*q^7 + 84*q^9 + 150*q^11 + 248*q^13 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*(eta[q^2]*eta[q^4]/(eta[q]*eta[q^8]))^4, {q, 0, 100}], q]; Table[a[[n]], {n, 1, 80}] (* _G. C. Greubel_, Jun 20 2018 *)
%o (PARI) q='q+O('q^50); Vec((eta(q^2)*eta(q^4)/(eta(q)*eta(q^8)))^4) \\ _G. C. Greubel_, Jun 20 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 20 2018
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