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%I #20 Jun 14 2018 11:56:16
%S 1,0,5,10,18,30,51,80,124,190,281,410,592,840,1178,1640,2253,3070,
%T 4154,5570,7422,9830,12932,16920,22028,28520,36761,47180,60280,76720,
%U 97278,122880,154693,194110,242776,302740,376424,466710,577114,711800,875707,1074790
%N McKay-Thompson series of class 20F for Monster.
%H G. C. Greubel, <a href="/A058555/b058555.txt">Table of n, a(n) for n = -1..5000</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 a(n) ~ exp(2*Pi*sqrt(n/5)) / (2*5^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Mar 21 2018
%F Expansion of -2 + (eta(q^4)*eta(q^5)/(eta(q)*eta(q^20)))^2 in powers of q. - _G. C. Greubel_, Jun 14 2018
%e T20F = 1/q + 5*q + 10*q^2 + 18*q^3 + 30*q^4 + 51*q^5 + 80*q^6 + 124*q^7 + ...
%t nmax = 50; QP=QPochhammer; CoefficientList[Series[-2*x + (QP[x^4] *QP[x^5]/(QP[x]*QP[x^20]))^2, {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Mar 21 2018 *)
%t eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(-2 + (eta[q^4]*eta[q^5]/(eta[q]*eta[q^20]))^2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 14 2018 *)
%o (PARI) q='q+O('q^50); A= -2 + (eta(q^4)*eta(q^5)/(eta(q)*eta(q^20)))^2/q; Vec(A) \\ _G. C. Greubel_, Jun 14 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 19 2014
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