A191803 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(5*n^2).

1, 1, 6, 61, 791, 11701, 188462, 3225915, 57840755, 1076423857, 20666351126, 407645638428, 8237858879315, 170229866493435, 3592746391559133, 77393340642273491, 1701286171473636404, 38169860244429063080

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^(5*n)*Product_{k=1..n} (1-x*A^(20*k-15))/(1-x*A^(20*k-5));

(2) A = 1/(1- A^5*x/(1- A^5*(A^10-1)*x/(1- A^25*x/(1- A^15*(A^20-1)*x/(1- A^45*x/(1- A^25*(A^30-1)*x/(1- A^65*x/(1- A^35*(A^40-1)*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 + 6*x^2 + 61*x^3 + 791*x^4 + 11701*x^5 + 188462*x^6 +...
where the g.f. satisfies:
A(x) = 1 + x*A(x)^5 + x^2*A(x)^20 + x^3*A(x)^45 + x^4*A(x)^80 +...+ x^n*A(x)^(5*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))^(5*m^2))); polcoeff(A, n)}

Crossrefs

Cf. A107595, A191800, A191801, A191802, A191804.

Sequence in context: A369509 A064088 A342110 * A259271 A047737 A302535

Adjacent sequences: A191800 A191801 A191802 * A191804 A191805 A191806

Keyword

nonn

Author

Paul D. Hanna, Jun 16 2011

Status

approved