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%I #18 Jun 28 2018 03:57:54
%S 1,0,1,4,6,6,10,10,19,22,32,40,51,68,86,108,135,166,218,258,325,390,
%T 477,582,713,856,1025,1222,1480,1750,2093,2470,2930,3458,4081,4782,
%U 5620,6550,7702,8960,10441,12110,14062,16298,18863,21776,25130,28884,33310
%N McKay-Thompson series of class 35A for Monster.
%H G. C. Greubel, <a href="/A058640/b058640.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^5)*eta(q^7)/(eta(q)*eta(q^35)), in powers of q. - _G. C. Greubel_, Jun 24 2018
%F a(n) ~ exp(4*Pi*sqrt(n/35)) / (sqrt(2) * 35^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018
%e T35A = 1/q + q + 4*q^2 + 6*q^3 + 6*q^4 + 10*q^5 + 10*q^6 + 19*q^7 + 22*q^8 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= eta[q^5]*eta[q^7]/( eta[q]* eta[q^35]); a:= CoefficientList[Series[q*(A - 1 - 1/A), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 24 2018 *)
%o (PARI) q='q+O('q^50); A = eta(q^5)*eta(q^7)/(q*eta(q)*eta(q^35)); Vec(A - 1 - 1/A) \\ _G. C. Greubel_, Jun 24 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,4
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Michel Marcus_, Feb 20 2014
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