%I #28 Jun 19 2018 12:31:23
%S 1,8,4372,96256,1240002,10698752,74428120,431529984,2206741887,
%T 10117578752,42616961892,166564106240,611800208702,2125795885056,
%U 7040425608760,22327393665024,68134255043715,200740384538624
%N McKay-Thompson series of class 2A for Monster.
%H Vincenzo Librandi, <a href="/A045478/b045478.txt">Table of n, a(n) for n = -1..500</a>
%H J. H. Conway and S. P. Norton, <a href="http://blms.oxfordjournals.org/content/11/3/308.extract">Monstrous Moonshine</a>, Bull. Lond. Math. Soc. 11 (1979) 308-339.
%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 J. McKay and H. Strauss, <a href="http://dx.doi.org/10.1080/00927879008823911">The q-series of monstrous moonshine and the decomposition of the head characters</a>, Comm. Algebra 18 (1990), no. 1, 253-278.
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F a(n) ~ exp(2*Pi*sqrt(2*n)) / (2^(3/4)*n^(3/4)). - _Vaclav Kotesovec_, Apr 01 2017
%F Expansion of (1 + 32*A + (64*A)^2)/A, where A = (eta(q^2)/eta(q))^24, in powers of q. - _G. C. Greubel_, Jun 19 2018
%t nmax = 30; CoefficientList[Series[32*x + 4096*x^2*Product[(1 + x^k)^24, {k, 1, nmax}] + Product[1/(1 + x^k)^24, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 01 2017 *)
%t eta[q_]:= q^(1/24)*QPochhammer[q]; A:= (eta[q^2]/eta[q])^24; a:= CoefficientList[Series[q*(1 + 32*A + 64^2*A^2)/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 19 2018 *)
%o (PARI) q='q+O('q^50); A = q*(eta(q^2)/eta(q))^24; Vec((1+32*A+(64*A)^2)/A) \\ _G. C. Greubel_, Jun 19 2018
%Y Cf. A007241, A007267.
%Y A045478, A007241, A106207, A007267, A101558 are all essentially the same sequence.
%K nonn,nice
%O -1,2
%A _N. J. A. Sloane_