A381783 G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * C(x*A(x)), where C(x) is the g.f. of A000108.

1, 2, 11, 79, 645, 5682, 52643, 505575, 4987933, 50250625, 514787110, 5346336739, 56161123273, 595667090038, 6370314162095, 68616488830785, 743733580011957, 8106009997644507, 88783190884441892, 976705067814061730, 10787334777299825522, 119569153425125828365

Offset

0,2

Links

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

Formula

a(n) = (1/(3*n+1)) * Sum_{k=0..n} binomial(3*n+1,k) * binomial(3*n-2*k+1,n-k).

Prog

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

Crossrefs

Cf. A212071, A381773, A381782.

Cf. A000108.

Sequence in context: A378670 A151418 A154273 * A396433 A253256 A163203

Adjacent sequences: A381780 A381781 A381782 * A381784 A381785 A381786

Keyword

nonn

Author

Seiichi Manyama, Mar 07 2025

Status

approved