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%I #27 Sep 16 2020 01:59:10
%S 1,0,0,1,1,1,2,1,2,2,2,2,4,3,4,5,5,5,8,7,8,10,10,11,15,14,16,19,20,21,
%T 27,26,30,35,36,39,47,47,52,60,63,68,80,81,90,101,106,114,132,135,148,
%U 165,174,187,212,219,239,264,279,299,334,348,377,414,438
%N McKay-Thompson series of class 87A for Monster.
%C Also McKay-Thompson series of class 87B for Monster. - _Michel Marcus_, Feb 24 2014
%H G. C. Greubel, <a href="/A058762/b058762.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 (1/4)*( -3 - T29A(q) - T29A(q^3) + sqrt((3 + T29A(q) + T29A(q^2))^2 + 8*(T29A(q)*T29A(q^3) - 3)) ) in powers of q, where T29A(q) is the g.f. of A058611. - _G. C. Greubel_, Jul 01 2018 [Corrected by _Sean A. Irvine_, Sep 16 2020]
%F a(n) ~ exp(4*Pi*sqrt(n/87)) / (sqrt(2) * 87^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 02 2018
%e T87A = 1/q + q^2 + q^3 + q^4 + 2*q^5 + q^6 + 2*q^7 + 2*q^8 + 2*q^9 + 2*q^10 + ...
%t QP := QPochhammer; nmax = 100;
%t f[x_, y_] := QP[-x, x*y]*QP[-y, x*y]* QP[x*y, x*y];
%t G[x_] := f[-x^2, -x^3]/f[-x, -x^2];
%t H[x_] := f[-x, -x^4]/f[-x, -x^2];
%t A := G[x^29]*G[x] + x^6*H[x^29]*H[x];
%t T29A := -2 + A^2/x;
%t T87A := (1/4)*( -3 - T29A - (T29A/.{x -> x^3}) + ((3 + T29A + (T29A/.{x -> x^3}))^2 + 8*( T29A*(T29A /. {x -> x^3}) - 3) + O[x]^nmax)^(1/2) );
%t a:= CoefficientList[Series[x*T87A, {x, 0, nmax}], x];
%t Table[a[[n]], {n, 1, nmax}] (* _G. C. Greubel_, Jul 01 2018 *)
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,7
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Michel Marcus_, Feb 24 2014
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