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%I #15 Jun 28 2018 03:36:00
%S 1,2,0,1,1,3,1,6,3,5,7,9,8,14,9,17,18,24,21,33,30,40,43,54,52,77,69,
%T 93,97,117,121,160,153,191,200,246,250,319,312,381,410,480,494,607,
%U 609,733,775,903,937,1120,1152,1345,1431,1638,1712,2020,2085,2406
%N McKay-Thompson series of class 60A for the Monster group.
%H G. C. Greubel, <a href="/A058725/b058725.txt">Table of n, a(n) for n = 0..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>, Comm. 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 Expansion of A + q/A, where A = q^(1/2)*(eta(q^2)*eta(q^3)*eta(q^10) *eta(q^15)/(eta(q)*eta(q^5)*eta(q^6)*eta(q^30))), in powers of q. - _G. C. Greubel_, Jun 28 2018
%F a(n) ~ exp(2*Pi*sqrt(n/15)) / (2 * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018
%e T60A = 1/q + 2*q + q^5 + q^7 + 3*q^9 + q^11 + 6*q^13 + 3*q^15 + 5*q^17 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]*eta[q^3]* eta[q^10]*eta[q^15]/(eta[q]*eta[q^5]*eta[q^6]*eta[q^30])); a:= SeriesCoefficient[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* _G. C. Greubel_, Jun 28 2018 *)
%o (PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^3)*eta(q^10)*eta(q^15)/(eta(q)* eta(q^5)*eta(q^6)*eta(q^30))); Vec(A + q/A) \\ _G. C. Greubel_, Jun 28 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Nov 27 2000
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