A177341 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(n(3n+1)/2).

1, 1, 3, 15, 94, 670, 5199, 42879, 370532, 3324129, 30770131, 292642516, 2851110772, 28396320852, 288716877223, 2994030992113, 31652050802267, 341066444176593, 3746408312358063, 41963633210168463, 479546389644040335

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

A = Sum_{n>=0} x^n*A^(2n)*Product_{k=1..n} (1-x*A^(6k-4))/(1-x*A^(6k-1)) due to a q-series identity.

G.f. A(x) satisfies: A(x) = B(x*A(x)) and A(x/B(x)) = B(x) where B(x) = g.f. of A177340.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 94*x^4 + 670*x^5 + 5199*x^6 +...
A(x) = 1 + x*A(x)^2 + x^2*A(x)^7 + x^3*A(x)^15 + x^4*A(x)^26 +...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*A^(j*(3*j+1)/2)+x*O(x^n))); polcoeff(A, n)}

Crossrefs

Cf. A177340.

Sequence in context: A368964 A274734 A378951 * A220262 A365560 A306027

Adjacent sequences: A177338 A177339 A177340 * A177342 A177343 A177344

Keyword

nonn

Author

Paul D. Hanna, May 06 2010

Status

approved