%I #11 Apr 01 2017 03:35:42
%S 1,-6,134,760,3345,12256,39350,114096,307060,776000,1867170,4298600,
%T 9540169,20487360,42756520,86967184,172859325,336450560,642489660,
%U 1205572920,2226005750,4049168800,7264172196,12864273920,22507811570,38936117376,66640520250
%N McKay-Thompson series of class 5A for the Monster group with a(0) = -6.
%H Seiichi Manyama, <a href="/A244745/b244745.txt">Table of n, a(n) for n = -1..10000</a>
%F Expansion of (eta(q) / eta(q^5))^6 + 125 * (eta(q^5) / eta(q))^6 in powers of q.
%F a(n) = A007251(n) = A045482(n) unless n = 0.
%F a(n) = A106248(n) + 125*A121591(n) for n > 0. - _Seiichi Manyama_, Mar 31 2017
%F a(n) ~ exp(4*Pi*sqrt(n/5)) / (sqrt(2)*5^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Apr 01 2017
%e G.f. = 1/q - 6 + 134*q + 760*q^2 + 3345*q^3 + 12256*q^4 + 39350*q^5 + ...
%t a[ n_] := With[{A = (QPochhammer[ q] / QPochhammer[ q^5])^6 / q}, SeriesCoefficient[ A + 125 / A, {q, 0, n}]];
%o (PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); A = (eta(x + A) / eta(x^5 + A))^6; polcoeff( A + x^2 * 125 / A, n))};
%Y Cf. A007251, A045482.
%Y Cf. A106248 ((eta(q) / eta(q^5))^6), A121591 ((eta(q^5) / eta(q))^6).
%K sign
%O -1,2
%A _Michael Somos_, Jul 05 2014