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%I #22 Jul 02 2018 06:43:25
%S 1,0,0,0,1,1,1,1,1,1,1,1,2,1,2,2,2,2,3,3,3,4,4,4,5,5,6,6,7,7,8,8,10,
%T 10,11,12,13,13,15,16,18,18,21,21,23,24,27,28,31,33,35,37,40,42,46,48,
%U 53,55,59,62,68,71,76,81,86,90,97,102,110,115,124,129
%N McKay-Thompson series of class 119A for Monster.
%H Vaclav Kotesovec, <a href="/A058776/b058776.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 in powers of q, where A = G(q^119)*G(q) + q^24*H(q^119)*H(q), B = G(q^17)*H(q^7) - q^2*H(q^17)*G(q^7), G() is g.f. of A003114 and H() is g.f. of A003106. - _G. C. Greubel_, Jul 01 2018
%F a(n) ~ exp(4*Pi*sqrt(n/119)) / (sqrt(2) * 119^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 02 2018
%e T119A = 1/q + q^3 + q^4 + q^5 + q^6 + q^7 + q^8 + q^9 + q^10 + 2*q^11 + q^12 + ...
%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^119]*G[x] + x^24*H[x^119]*H[x]; B:= G[x^17]*H[x^7] - x^2*H[x^17]*G[x^7]; a:= CoefficientList[Series[-x + A*B, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jul 01 2018 *)
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,13
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Michel Marcus_, Feb 19 2014
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