A381782 G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * C(x), where C(x) is the g.f. of A000108.

1, 2, 9, 52, 342, 2437, 18331, 143320, 1153308, 9489487, 79470647, 675149665, 5804359859, 50402807459, 441433999816, 3894774605660, 34585663823538, 308867647484634, 2772256164853972, 24994569816424301, 226261997160303326, 2055711320495566962

Offset

0,2

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A212071, A381773, A381783.

Cf. A000108.

Sequence in context: A003584 A301928 A069271 * A305987 A355789 A231494

Adjacent sequences: A381778 A381779 A381780 * A381783 A381784 A381785

Keyword

nonn,new

Author

Seiichi Manyama, Mar 07 2025

Status

approved