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%I #18 Jun 29 2018 09:42:29
%S 1,1,1,3,2,3,6,5,7,12,12,15,21,21,27,36,40,48,62,69,81,102,112,132,
%T 164,183,212,258,286,330,396,440,507,600,668,765,893,994,1133,1311,
%U 1462,1659,1906,2123,2396,2736,3044,3423,3893,4324,4848,5487,6080,6798,7660,8478,9457,10614
%N McKay-Thompson series of class 48A for Monster.
%H G. C. Greubel, <a href="/A058691/b058691.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>, 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 q^(1/2)*(eta(q^2)*eta(q^4)* eta(q^6)*eta(q^12)/(eta(q)* eta(q^3)*eta(q^8)*eta(q^24))) in powers of q. - _G. C. Greubel_, Jun 27 2018
%F a(n) ~ exp(Pi*sqrt(n/3)) / (2^(3/2) * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018
%e T48A = 1/q + q + q^3 + 3*q^5 + 2*q^7 + 3*q^9 + 6*q^11 + 5*q^13 + 7*q^15 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]*eta[q^4]* eta[q^6]*eta[q^12]/(eta[q]*eta[q^3]*eta[q^8]*eta[q^24])); a:= CoefficientList[Series[A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 27 2018 *)
%o (PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^4)* eta(q^6)*eta(q^12)/(eta(q)* eta(q^3)*eta(q^8)*eta(q^24))); Vec(A) \\ _G. C. Greubel_, Jun 27 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,4
%A _N. J. A. Sloane_, Nov 27 2000
%E Terms a(12) onward added by _G. C. Greubel_, Jun 27 2018
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