OFFSET
-1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = -1..10000
Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction
FORMULA
Expansion of (eta(q) / eta(q^5))^6 in powers of q.
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).
Convolution inverse of A121591.
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
EXAMPLE
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 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ 1/q (QPochhammer[ q] / QPochhammer[ q^5])^6, {q, 0, n}]; (* Michael Somos, May 22 2013 *)
PROG
(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))};
(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))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Apr 26 2005
STATUS
approved