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%I #19 Jul 05 2018 03:22:39
%S 1,0,1,2,2,1,3,2,3,5,5,5,8,7,10,13,12,14,19,19,23,28,31,33,43,43,51,
%T 60,65,71,87,91,104,121,130,144,171,180,202,232,250,274,318,338,378,
%U 426,461,506,575,613,680,759,821,897,1007,1080,1187,1316,1423,1550,1721,1847,2022,2226
%N McKay-Thompson series of class 66a for Monster.
%H G. C. Greubel, <a href="/A058741/b058741.txt">Table of n, a(n) for n = -1..1499</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 sqrt(T33B) in powers of q, where T33B = A058637. - _G. C. Greubel_, Jul 03 2018
%F a(n) ~ exp(2*Pi*sqrt(2*n/33)) / (2^(3/4) * 33^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 05 2018
%e T66a = 1/q + q^3 + 2*q^5 + 2*q^7 + q^9 + 3*q^11 + 2*q^13 + 3*q^15 + 5*q^17 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; A := eta[q]*eta[q^11]/ (eta[q^3]*eta[q^33]); a:= CoefficientList[Series[ (q*(1 + A + 3/A) + O[q]^nmax)^(1/2), {q, 0, 90}], q]; Table[a[[n]], {n, 1, 80}] (* _G. C. Greubel_, Jul 03 2018 *)
%o (PARI) q='q+O('q^80); A = eta(q)*eta(q^11)/(q*eta(q^3)*eta(q^33)); Vec(sqrt(q*(A + 1 + 3/A))) \\ _G. C. Greubel_, Jul 03 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,4
%A _N. J. A. Sloane_, Nov 27 2000
%E Terms a(12) onward added by _G. C. Greubel_, Jul 03 2018
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