A153292 G.f.: A(x) = F(x*F(x)^2) where F(x) = 1 + x*F(x)^3 is the g.f. of A001764.

1, 1, 5, 31, 211, 1516, 11295, 86423, 675051, 5361323, 43171480, 351709926, 2894115003, 24022408477, 200918146461, 1691749323232, 14329850844625, 122028162988698, 1044131083377287, 8972696721635997, 77408293908402336

Offset

0,3

Links

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

Formula

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

G.f. satisfies: A(x) = 1 + x*F(x)^2*A(x)^3 where F(x) is the g.f. of A001764.

G.f. satisfies: A(x/G(x)) = F(x*G(x)) where G(x) = F(x/G(x)) is the g.f. of A000108 and F(x) is the g.f. of A001764.

Example

G.f.: A(x) = F(x*F(x)^2) = 1 + x + 5*x^2 + 31*x^3 + 211*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 +...

Prog

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

Crossrefs

Cf. A001764, A000108; A153293.

Sequence in context: A247639 A002649 A104091 * A087457 A146962 A269730

Adjacent sequences: A153289 A153290 A153291 * A153293 A153294 A153295

Keyword

nonn

Author

Paul D. Hanna, Jan 14 2009

Status

approved