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%I #27 Apr 16 2017 04:56:23
%S 1,0,14,36,85,180,360,684,1246,2196,3754,6264,10226,16380,25804,40032,
%T 61275,92628,138452,204804,300040,435672,627356,896400,1271525,
%U 1791324,2507426,3488472,4825531,6638688,9085888,12373992,16772908,22633812
%N McKay-Thompson series of class 12H for Monster.
%H G. A. Edgar, <a href="/A058486/b058486.txt">Table of n, a(n) for n = -1..1002</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 Given g.f. A(x), then B(x) = A(x)+4 satisfies 0 = f(B(x), B(x^2)) where f(u, v) = -u*v*(1 + u^2*v^2) + 7*u*v*(u + v)*(1 + u*v) + 9*u*v*(u^2 + v^2). - _Michael Somos_, May 16 2004
%F Expansion of (eta(q^3) * eta(q^4) / (eta(q) * eta(q^12)))^4 - 4 in powers of q. - _Michael Somos_, May 16 2004
%F a(n) ~ exp(2*Pi*sqrt(n/3)) / (2 * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 11 2016
%e T12H = 1/q + 14*q + 36*q^2 + 85*q^3 + 180*q^4 + 360*q^5 + 684*q^6 + ...
%t QP = QPochhammer; s = (QP[q^3]*(QP[q^4]/(QP[q]*QP[q^12])))^4 - 4*q + O[q]^40; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 13 2015, adapted from PARI *)
%o (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x^3 + A) * eta(x^4 + A) / (eta(x + A) * eta(x^12 + A)))^4 - 4*x, n))}; /* _Michael Somos_, May 16 2004 */
%o (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x^2 + A)^6 * eta(x^6 + A)^6 / (eta(x + A)^5 * eta(x^3 + A) * eta(x^4 + A) * eta(x^12 + A)^5) - 5*x, n))}; /* _Michael Somos_, May 16 2004 */
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,3
%A _N. J. A. Sloane_, Nov 27 2000
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