A381778 G.f. A(x) satisfies A(x) = (1 + x*A(x)) * C(x*A(x)^2), where C(x) is the g.f. of A000108.

1, 2, 9, 60, 474, 4105, 37681, 360122, 3545320, 35705553, 366126614, 3809497971, 40119258081, 426829897847, 4580629916321, 49527776299522, 539025763347730, 5900193301962178, 64913644702760248, 717433047054489969, 7961616716665723173, 88679610762886209459

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} binomial(n+3*k+1,k) * binomial(n+k+1,n-k)/(n+3*k+1).

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(n+k+1, n-k)/(n+3*k+1));

Crossrefs

Cf. A054727, A381779.

Cf. A000108.

Sequence in context: A156272 A366240 A363390 * A205570 A381300 A116364

Adjacent sequences: A381775 A381776 A381777 * A381779 A381780 A381782

Keyword

nonn,new

Author

Seiichi Manyama, Mar 07 2025

Status

approved