%I #19 Jun 28 2018 10:06:19
%S 1,0,2,1,2,2,5,4,7,7,12,10,17,16,25,24,35,34,51,49,69,70,96,96,130,
%T 132,175,180,231,240,308,320,402,423,526,552,680,718,877,928,1120,
%U 1190,1430,1520,1809,1932,2285,2440,2870,3072,3594,3850,4477,4802,5565
%N McKay-Thompson series of class 50A for Monster.
%H G. C. Greubel, <a href="/A058701/b058701.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 A - 1 + 1/A, where A = eta(q^2)*eta(q^25)/(eta(q)*eta(q^50) ), in powers of q. - _G. C. Greubel_, Jun 27 2018
%F a(n) ~ exp(2*Pi*sqrt(2*n)/5) / (2^(3/4) * sqrt(5) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018
%e T50A = 1/q + 2*q + q^2 + 2*q^3 + 2*q^4 + 5*q^5 + 4*q^6 + 7*q^7 + 7*q^8 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= (eta[q^2]*eta[q^25]/( eta[q]* eta[q^50])); a:= CoefficientList[Series[-1 + A + 1/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 27 2018 *)
%o (PARI) q='q+O('q^50); A = eta(q^2)*eta(q^25)/(q*eta(q)*eta(q^50)); Vec(A - 1 + 1/A) \\ _G. C. Greubel_, Jun 27 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 24 2014
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