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A058484 McKay-Thompson series of class 12F for Monster.

%I A058484 #24 Jul 02 2018 20:25:35
%S A058484 1,6,21,56,126,258,498,924,1659,2884,4872,8028,12965,20586,32187,
%T A058484 49616,75468,113412,168590,248148,361929,523348,750660,1068576,
%U A058484 1510428,2120934,2959692,4105808,5663814,7771452,10609576,14414676,19494855,26249984,35197536
%N A058484 McKay-Thompson series of class 12F for Monster.
%H A058484 Vaclav Kotesovec, <a href="/A058484/b058484.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..148 from G. A. Edgar)
%H A058484 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 A058484 <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F A058484 a(n) ~ exp(2*Pi*sqrt(n/3)) / (2 * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Sep 10 2015
%F A058484 From _G. A. Edgar_, Mar 13 2017: (Start)
%F A058484 Expansion of q^(1/2)*(eta(q^2)*eta(q^3) / (eta(q)*eta(q^6)))^6 in powers of q.
%F A058484 T12F(q) = T6B(q^2)^(1/2) with T6B the g.f. of A121665, the convolution square of A058484. (End)
%e A058484 T12F = 1/q + 6*q + 21*q^3 + 56*q^5 + 126*q^7 + 258*q^9 + 498*q^11 + ...
%t A058484 nmax = 50; CoefficientList[Series[Product[((1+x^(3*k-1))*(1+x^(3*k-2)))^6, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 10 2015 *)
%t A058484 eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]*eta[q^3]/(eta[q]*eta[q^6]))^6; a := CoefficientList[Series[A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jul 01 2018 *)
%o A058484 (PARI)q='q+O('q^66); Vec( eta(q^2)^6*eta(q^3)^6 / (eta(q)^6*eta(q^6)^6) )  \\ _Joerg Arndt_, Mar 13 2017
%Y A058484 Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K A058484 nonn
%O A058484 0,2
%A A058484 _N. J. A. Sloane_, Nov 27 2000
%E A058484 More terms from _Vaclav Kotesovec_, Sep 10 2015