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%I #19 Jun 27 2018 10:00:25
%S 1,0,2,2,5,4,9,8,16,16,25,26,44,44,67,70,103,108,155,166,230,248,333,
%T 362,482,524,680,748,959,1052,1330,1468,1834,2028,2500,2770,3394,3760,
%U 4561,5066,6100,6772,8102,9000,10702,11888,14048,15612,18360,20396,23865
%N McKay-Thompson series of class 38A for Monster.
%H G. C. Greubel, <a href="/A058657/b058657.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 -1/2 + (17/4 + T19A(q) + T19A(q^2) )^(1/2), where T19A(q) = A058549, in powers of q. - _G. C. Greubel_, Jun 24 2018
%F a(n) ~ exp(2*Pi*sqrt(2*n/19)) / (2^(3/4) * 19^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 27 2018
%e T38A = 1/q + 2*q + 2*q^2 + 5*q^3 + 4*q^4 + 9*q^5 + 8*q^6 + 16*q^7 + 16*q^8 + ...
%t QP := QPochhammer; eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; G[q_] := 1/(QP[q, q^5]*QP[q^4, q^5]); H[q_] := 1/(QP[q^2, q^5]*QP[q^3, q^5]); T19A := -3 + (G[q]*G[q^19] + q^4*H[q]*H[q^19])^3/q; a:= CoefficientList[Series[q*(-1/2 + (17/4 + T19A + (T19A /. {q -> q^2}) + O[q]^nmax)^(1/2)), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 24 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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