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%I #23 Jun 29 2018 12:06:56
%S 1,0,1,2,2,2,5,4,6,8,9,10,17,16,19,26,29,34,46,48,59,72,80,92,117,126,
%T 148,178,198,226,274,298,345,404,450,510,601,660,753,866,965,1084,
%U 1253,1378,1558,1770,1965,2196,2501,2752,3085,3476,3845,4276,4820,5298
%N McKay-Thompson series of class 51A for the Monster group.
%H Vaclav Kotesovec, <a href="/A058704/b058704.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 A*B in powers of q, where A = G(q^17)*G(q^3) + q^4*H(q^17) *H(q^3), B = G(q^51)*H(q) - q^10*H(q^51)*G(q), G() is g.f. of A003114 and H() is g.f. of A003106. - _G. C. Greubel_, Jun 29 2018
%F a(n) ~ exp(4*Pi*sqrt(n/51)) / (sqrt(2) * 51^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 29 2018
%e T51A = 1/q + q + 2*q^2 + 2*q^3 + 2*q^4 + 5*q^5 + 4*q^6 + 6*q^7 + 8*q^8 + ...
%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^17]*G[x^3] + x^4*H[x^17]*H[x^3]; B := G[x^51]*H[x] - x^10*H[x^51]*G[x]; a := CoefficientList[Series[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 -1,4
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Michel Marcus_, Feb 24 2014
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