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).

a(n) ~ sqrt(43/((111*sqrt(129) - 1247)*Pi)) * 2^(5*n) / (3 * n^(3/2) * (93*sqrt(129) - 1053)^n). - Vaclav Kotesovec, Jun 06 2026

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, A007852.

Sequence in context: A394146 A069271 A394157 * A305987 A355789 A231494

Adjacent sequences: A381779 A381780 A381781 * A381783 A381784 A381785

Keyword

nonn

Author

Seiichi Manyama, Mar 07 2025

Status

approved