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%I #30 Jul 05 2018 14:00:07
%S 1,0,1,1,1,1,2,2,3,3,4,4,6,6,7,8,10,11,13,14,17,19,22,24,29,31,36,40,
%T 46,50,58,63,72,79,89,98,111,121,136,149,167,182,204,222,247,270,299,
%U 326,362,393,434,473,521,566,623,676,742,806,882,956,1047,1133
%N McKay-Thompson series of class 71A for Monster.
%C Also McKay-Thompson series of class 71B for Monster. - _Michel Marcus_, Feb 19 2014
%H G. C. Greubel, <a href="/A034322/b034322.txt">Table of n, a(n) for n = -1..2500</a>
%H I. Chen and N. Yui, <a href="http://people.math.sfu.ca/~ichen/pub/chen-yui.pdf">Singular values of Thompson series</a>. In Groups, difference sets and the Monster (Columbus, OH, 1993), pp. 255-326, Ohio State University Mathematics Research Institute Publications, 4, de Gruyter, Berlin, 1996.
%H J. H. Conway and S. P. Norton, <a href="http://blms.oxfordjournals.org/content/11/3/308.extract">Monstrous Moonshine</a>, Bull. Lond. Math. Soc. 11 (1979) 308-339.
%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 a(n) ~ exp(4*Pi*sqrt(n/71)) / (sqrt(2) * 71^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 05 2018
%e T71A = 1/q + q + q^2 + q^3 + q^4 + 2*q^5 + 2*q^6 + 3*q^7 + 3*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:= CoefficientList[Series[G[x^71]*H[x] - x^14*H[x^71]*G[x], {x, 0, 80}], x]; Table[a[[n]], {n, 1, 70}] (* _G. C. Greubel_, Jul 05 2018 *)
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,7
%A _N. J. A. Sloane_
%E More terms from _Michel Marcus_, Feb 18 2014
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