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%I #18 Jul 04 2018 14:07:05
%S 1,0,2,2,3,4,7,8,11,14,19,22,30,36,46,56,70,84,106,124,153,182,221,
%T 260,314,368,440,516,611,712,842,976,1145,1326,1547,1784,2075,2386,
%U 2761,3168,3651,4178,4802,5478,6272,7144,8155,9264,10550,11956,13579,15362
%N McKay-Thompson series of class 41A for Monster.
%H G. C. Greubel, <a href="/A058670/b058670.txt">Table of n, a(n) for n = -1..2500</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 (G(q^41)*H(q) - q^8*H(q^41)*G(q))^2, in powers of q, where G() is g.f. of A003114 and H() is g.f. of A003106. - _G. C. Greubel_, Jul 03 2018
%F a(n) ~ exp(4*Pi*sqrt(n/41)) / (sqrt(2) * 41^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 04 2018
%e T41A = 1/q + 2*q + 2*q^2 + 3*q^3 + 4*q^4 + 7*q^5 + 8*q^6 + 11*q^7 + 14*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]; b:= G[x^41]*H[x] - x^8*H[x^41]*G[x]; a:= CoefficientList[Series[b^2, {x, 0, 90}], x]; Table[a[[n]], {n, 1, 80}] (* _G. C. Greubel_, Jul 03 2018 *)
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,3
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Michel Marcus_, Feb 20 2014
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