A191801 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(3*n^2).

1, 1, 4, 28, 251, 2573, 28813, 343833, 4308210, 56154805, 756731761, 10499096630, 149551069156, 2182935186698, 32613646656198, 498420592612153, 7790219357236805, 124545937719356873, 2037614647316548891, 34134979366157116560

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

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

(1) A = Sum_{n>=0} x^n*A^(3*n)*Product_{k=1..n} (1-x*A^(12*k-9))/(1-x*A^(12*k-3));

(2) A = 1/(1- A^3*x/(1- A^3*(A^6-1)*x/(1- A^15*x/(1- A^9*(A^12-1)*x/(1- A^27*x/(1- A^15*(A^18-1)*x/(1- A^39*x/(1- A^21*(A^24-1)*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 + 4*x^2 + 28*x^3 + 251*x^4 + 2573*x^5 + 28813*x^6 +...
where the g.f. satisfies:
A(x) = 1 + x*A(x)^3 + x^2*A(x)^12 + x^3*A(x)^27 + x^4*A(x)^48 +...+ x^n*A(x)^(3*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))^(3*m^2))); polcoeff(A, n)}

Crossrefs

Cf. A107595, A191800, A191802, A191803, A191804.

Sequence in context: A371693 A230640 A300050 * A365562 A379993 A064340

Adjacent sequences: A191798 A191799 A191800 * A191802 A191803 A191804

Keyword

nonn

Author

Paul D. Hanna, Jun 16 2011

Status

approved