A191804 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(6*n^2).

1, 1, 7, 82, 1221, 20718, 382315, 7489683, 153551487, 3264643144, 71545452946, 1609541143713, 37065029428453, 872037022019930, 20935244357544798, 512498682139660135, 12790021472251565047, 325439165493879484025

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

Let A = g.f. A(x), then A satisfies:

(1) A = Sum_{n>=0} x^n*A^(6*n)*Product_{k=1..n} (1-x*A^(24*k-18))/(1-x*A^(24*k-6));

(2) A = 1/(1- A^6*x/(1- A^6*(A^12-1)*x/(1- A^30*x/(1- A^18*(A^24-1)*x/(1- A^54*x/(1- A^30*(A^36-1)*x/(1- A^78*x/(1- A^42*(A^48-1)*x/(1- ...))))))))) (continued fraction);

due to a q-series identity and an identity of a partial elliptic theta function, respectively.

Example

 G.f.: A(x) = 1 + x + 7*x^2 + 82*x^3 + 1221*x^4 + 20718*x^5 + 382315*x^6 +...
where the g.f. satisfies:
A(x) = 1 + x*A(x)^6 + x^2*A(x)^24 + x^3*A(x)^54 + x^4*A(x)^96 +...+ x^n*A(x)^(6*n^2) +...

Prog

 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, x^m*(A+x*O(x^n))^(6*m^2))); polcoeff(A, n)}

Crossrefs

Cf. A107595, A191800, A191801, A191802, A191803.

Sequence in context: A338684 A304870 A361714 * A243672 A367424 A268653

Adjacent sequences: A191801 A191802 A191803 * A191805 A191806 A191807

Keyword

nonn

Author

Paul D. Hanna, Jun 16 2011

Status

approved