Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #20 Jul 02 2018 06:44:13
%S 1,0,1,1,1,1,3,2,2,4,4,4,7,6,8,10,10,11,16,15,18,22,24,26,34,34,39,47,
%T 50,56,69,70,80,93,100,110,131,137,154,176,189,208,241,254,283,320,
%U 345,377,430,456,505,563,607,661,744,793,871,964,1039,1129,1257
%N McKay-Thompson series of class 69A for Monster.
%C Also McKay-Thompson series of class 69B for Monster. - _Michel Marcus_, Feb 24 2014
%H Vaclav Kotesovec, <a href="/A058743/b058743.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/q, where A = G(q^69)*G(q) + q^14*H(q^69)*H(q), B = G(q^23)*H(q^3) - q^4*H(q^23)*G(q^3), G() is g.f. of A003114 and H() is g.f. of A003106. - _G. C. Greubel_, Jun 30 2018
%F a(n) ~ exp(4*Pi*sqrt(n/69)) / (sqrt(2) * 69^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 02 2018
%e T69A = 1/q + q + q^2 + q^3 + q^4 + 3*q^5 + 2*q^6 + 2*q^7 + 4*q^8 + 4*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^69]*G[x] + x^14*H[x^69]*H[x]; B:= G[x^23]*H[x^3] - x^4*H[x^23]*G[x^3]; a:= CoefficientList[Series[-1*x + A*B, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 30 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