%I #20 Jun 28 2018 04:04:10
%S 1,0,5,6,16,20,41,50,97,116,197,246,397,492,753,932,1378,1712,2434,
%T 3028,4210,5204,7075,8750,11692,14396,18943,23256,30220,36968,47477,
%U 57890,73614,89448,112726,136564,170734,206136,255872,308000,379801,455828,558714
%N McKay-Thompson series of class 22A for Monster.
%H G. C. Greubel, <a href="/A058567/b058567.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 David A. Madore, <a href="http://mathforum.org/kb/thread.jspa?forumID=253&threadID=1602206&messageID=5836094">Coefficients of Moonshine (McKay-Thompson) series</a>, The Math Forum
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F Expansion of A + 2 + 4/A, where A = (eta(q)*eta(q^11)/(eta(q^2)*eta(q^22) ))^2, in powers of q. - _G. C. Greubel_, Jun 21 2018
%F a(n) ~ exp(2*Pi*sqrt(2*n/11)) / (2^(3/4) * 11^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018
%e T22A = 1/q + 5*q + 6*q^2 + 16*q^3 + 20*q^4 + 41*q^5 + 50*q^6 + 97*q^7 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; A := (eta[q]*eta[q^11]/(eta[q^2]* eta[q^22]))^2; a:= CoefficientList[Series[q*(2 + A + 4/A), {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)*eta(q^11)/(eta(q^2)*eta(q^22)))^2/q; Vec(A + 2 + 4/A) \\ _G. C. Greubel_, Jun 21 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,3
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Michel Marcus_, Feb 20 2014