A191802 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(4*n^2).

1, 1, 5, 43, 473, 5942, 81393, 1186342, 18132473, 287948903, 4722077279, 79636530163, 1377304530677, 24382127678100, 441294262119031, 8160739579770316, 154169018332135841, 2975846752734820345, 58718914018159811186

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

(1) A = Sum_{n>=0} x^n*A^(4*n)*Product_{k=1..n} (1-x*A^(16*k-12))/(1-x*A^(16*k-4));

(2) A = 1/(1- A^4*x/(1- A^4*(A^8-1)*x/(1- A^20*x/(1- A^12*(A^16-1)*x/(1- A^36*x/(1- A^20*(A^24-1)*x/(1- A^52*x/(1- A^28*(A^32-1)*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 + 5*x^2 + 43*x^3 + 473*x^4 + 5942*x^5 + 81393*x^6 +...
where the g.f. satisfies:
A(x) = 1 + x*A(x)^4 + x^2*A(x)^16 + x^3*A(x)^36 + x^4*A(x)^64 +...+ x^n*A(x)^(4*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))^(4*m^2))); polcoeff(A, n)}

Crossrefs

Cf. A107595, A191800, A191801, A191803, A191804.

Sequence in context: A274666 A301976 A083070 * A092471 A093620 A231277

Adjacent sequences: A191799 A191800 A191801 * A191803 A191804 A191805

Keyword

nonn

Author

Paul D. Hanna, Jun 16 2011

Status

approved