A192619 G.f. satisfies: A(x) = Product_{n>=1} (1 + x^n*A(x)^(1/2))^2/(1 - x^n*A(x)^(1/2))^2.

1, 4, 20, 104, 556, 3048, 17064, 97216, 562036, 3289836, 19461448, 116178600, 699045176, 4235292680, 25816944176, 158223753376, 974389668364, 6026623271840, 37420762694588, 233179517592232, 1457706542138344, 9139698522931008

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

Self-convolution of A190862.

Example

G.f.: A(x) = 1 + 4*x + 20*x^2 + 104*x^3 + 556*x^4 + 3048*x^5 +...
The g.f. A = A(x) satisfies:
A = (1+x*A^(1/2))^2/(1-x*A^(1/2))^2 * (1+x^2*A^(1/2))^2/(1-x^2*A^(1/2))^2 * (1+x^3*A^(1/2))^2/(1-x^3*A^(1/2))^2 *...

Prog

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

Crossrefs

Cf. A190862.

Sequence in context: A104550 A089382 A291089 * A026305 A195256 A131786

Adjacent sequences: A192616 A192617 A192618 * A192620 A192621 A192622

Keyword

nonn

Author

Paul D. Hanna, Jul 06 2011

Status

approved