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%I #25 May 10 2018 02:50:23
%S 1,0,3,2,3,6,10,12,15,22,30,36,44,60,78,96,117,150,190,228,276,340,
%T 420,504,603,732,885,1052,1245,1488,1770,2088,2454,2902,3420,3996,
%U 4666,5460,6378,7400,8583,9972,11566,13344,15378,17752,20448,23472,26904,30876
%N McKay-Thompson series of class 36A for Monster.
%C A058533, A123676, A215412, A058644, A215413, A227585 are all essentially the same sequence. - _N. J. A. Sloane_, Aug 09 2012
%H G. C. Greubel, <a href="/A058644/b058644.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 <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)/3) / (2*sqrt(3)*n^(3/4)). - _Vaclav Kotesovec_, Sep 08 2017
%e T36A = 1/q + 3*q + 2*q^2 + 3*q^3 + 6*q^4 + 10*q^5 + 12*q^6 + 15*q^7 + ...
%t eta[q_]:= q^(1/24)*QPochhammer[q]; e36B2:= eta[q]*eta[q^4]*eta[q^18]/( eta[q^2]*eta[q^9]*eta[q^36]); T36A := 1 +e36B2 +3/e36B2; a:= CoefficientList[Series[q*T36A, {q,0,50}], q]; Table[a[[n]], {n,1,50}] (* _G. C. Greubel_, May 09 2018 *)
%o (PARI) q='q+O('q^50); Vec(1 + (eta(q)*eta(q^4)*eta(q^18)/(eta(q^2) *eta(q^9)*eta(q^36)))/q + 3*q*(eta(q^2)*eta(q^9)*eta(q^36)/(eta(q) *eta(q^4)*eta(q^18)))) \\ _G. C. Greubel_, May 09 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 18 2014
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