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%I #22 Jun 29 2018 12:12:14
%S 1,0,1,1,3,2,4,3,6,5,9,8,14,12,19,18,27,26,37,36,52,50,69,68,93,93,
%T 122,124,162,164,210,216,274,281,351,364,451,468,572,598,726,760,913,
%U 960,1148,1208,1431,1512,1782,1884,2206,2339,2727,2892,3353,3564,4114
%N McKay-Thompson series of class 54A for the Monster group.
%H Vaclav Kotesovec, <a href="/A058708/b058708.txt">Table of n, a(n) for n = -1..10000</a> (terms -1..2500 from G. C. Greubel)
%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 -1 + A*B/x in powers of q, where A = G(x^54)*G(x) + x^11* H(x^54)*H(x), B = G(x^27)*H(x^2) - x^5*H(x^27)*G(x^2), G() is g.f. of A003114 and H() is g.f. of A003106. - _G. C. Greubel_, Jun 29 2018
%F a(n) ~ exp(2*Pi*sqrt(2*n/3)/3) / (6^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 29 2018
%e T54A = 1/q + q + q^2 + 3*q^3 + 2*q^4 + 4*q^5 + 3*q^6 + 6*q^7 + 5*q^8 + 9*q^9 + ...
%t QP := QPochhammer; f[x_, y_] := QP[-x, x*y]*QP[-y, x*y]*QP[x*y, x*y]; G[x_] := f[-x^2, -x^3]/f[-x, -x^2]; H[x_] := f[-x, -x^4]/f[-x, -x^2]; A:= G[x^54]*G[x^1] + x^11*H[x^54]*H[x^1]; B:= G[x^27]*H[x^2] - x^5*H[x^27]*G[x^2]; a:= CoefficientList[Series[-x + A*B, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 29 2018 *)
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,5
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Michel Marcus_, Feb 24 2014
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