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%I #33 Oct 23 2017 13:05:07
%S 1,-6,9,10,-30,6,-25,96,60,-250,45,-150,544,360,-1230,184,-675,2310,
%T 1410,-4830,750,-2450,8196,4920,-16180,2376,-7875,25644,15000,-48720,
%U 7126,-22800,73221,42310,-134760,19284,-61400,194334,110610,-349000,49563,-155250,486370
%N McKay-Thompson series of class 5B for the Monster group with a(0) = -6.
%H Seiichi Manyama, <a href="/A106248/b106248.txt">Table of n, a(n) for n = -1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rogers-RamanujanContinuedFraction.html">Rogers-Ramanujan Continued Fraction</a>
%F Expansion of (eta(q) / eta(q^5))^6 in powers of q.
%F G.f. A(x) satisfies: 0 = f(A(x), A(x^2)) where f(u, v) = u*v * (u*v + 125) - (u+v) * (u^2 - 13 * u*v + v^2).
%F a(n) = A007252(n) = A045483(n) unless n=0.
%F Convolution inverse of A121591.
%F a(n) = A229793(n) - A078905(n) for n > 0. - _Seiichi Manyama_, Jan 01 2017
%F a(-1) = 1, a(n) = -(6/(n+1))*Sum_{k=1..n+1} A116073(k)*a(n-k) for n > -1. - _Seiichi Manyama_, Mar 29 2017
%e G.f. = 1/q - 6 + 9*q + 10*q^2 - 30*q^3 + 6*q^4 - 25*q^5 + 96*q^6 + 60*q^7 + ...
%t a[ n_] := SeriesCoefficient[ 1/q (QPochhammer[ q] / QPochhammer[ q^5])^6, {q, 0, n}]; (* _Michael Somos_, May 22 2013 *)
%o (PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x + A) / eta(x^5 + A))^6, n))};
%o (PARI) {a(n) = my(A, k); if( n<-1, 0, k = (sqrtint(40*n + 48) + 7)\10; A = x * (sum(i=-k, k, (-1)^i * x^((5*i^2 + 3*i)/2), x^2 * O(x^n)) / sum(i=-k, k, (-1)^i * x^((5*i^2 + i)/2), x^2 * O(x^n)))^5; polcoeff( 1 / A - 11 - A, n))};
%Y Cf. A007252, A121591.
%Y Cf. A045483. [_R. J. Mathar_, Dec 13 2008]
%Y Cf. A058511, A078905, A145466, A229793.
%K sign
%O -1,2
%A _Michael Somos_, Apr 26 2005
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