A153390 G.f.: A(x) = F(x*G(x))^2 where F(x) = G(x*F(x)) = 1 + x*F(x)^3 is the g.f. of A001764 and G(x) = F(x/G(x)) = 1 + x*G(x)^2 is the g.f. of A000108 (Catalan).

1, 2, 9, 48, 278, 1696, 10736, 69886, 465019, 3149476, 21643433, 150554144, 1058101315, 7502183626, 53599160532, 385494328218, 2788827078507, 20280590381098, 148167425970522, 1087007419753186, 8004683588800899

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} C(3k+2,k)*2/(3k+2) * C(2n-k,n-k)*k/(2n-k) for n>0 with a(0)=1.

G.f. satisfies: A(x*F(x)) = F(x*F(x)^2)^2 where F(x) is the g.f. of A001764.

Example

G.f.: A(x) = F(x*G(x))^2 = 1 + 2*x + 9*x^2 + 48*x^3 + 278*x^4 +... where
F(x) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*x^6 +...
F(x)^2 = 1 + 2*x + 7*x^2 + 30*x^3 + 143*x^4 + 728*x^5 + 3876*x^6 +...
F(x)^3 = 1 + 3*x + 12*x^2 + 55*x^3 + 273*x^4 + 1428*x^5 + 7752*x^6 +...
G(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 +...
G(x)^2 = 1 + 2*x + 5*x^2 + 14*x^3 + 42*x^4 + 132*x^5 + 429*x^6 +...

Prog

(PARI) {a(n)=if(n==0, 1, sum(k=0, n, binomial(3*k+2, k)*2/(3*k+2)*binomial(2*(n-k)+k, n-k)*k/(2*(n-k)+k)))}

Crossrefs

Cf. A000108, A001764; A153299, A153391.

Sequence in context: A047059 A153297 A364734 * A118341 A365133 A171803

Adjacent sequences: A153387 A153388 A153389 * A153391 A153392 A153393

Keyword

nonn

Author

Paul D. Hanna, Jan 15 2009

Status

approved