A381937 G.f. A(x) satisfies A(x) = (1 + x) * B(x*A(x)), where B(x) is the g.f. of A001764.

1, 2, 6, 35, 240, 1805, 14386, 119365, 1020136, 8918423, 79380514, 716911887, 6553219720, 60513355786, 563648995020, 5289485238552, 49963186247220, 474655663418546, 4532279676629700, 43473774550929628, 418706702628897708, 4047555977981218963

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} binomial(4*k+1,k) * binomial(k+1,n-k)/(4*k+1).

a(n) = A365178(n) + A365178(n-1).

Prog

(PARI) a(n) = sum(k=0, n, binomial(4*k+1, k)*binomial(k+1, n-k)/(4*k+1));

Crossrefs

Cf. A025227, A381787, A381940.

Cf. A001764, A346646, A365178.

Sequence in context: A018983 A279736 A081003 * A038181 A305275 A326090

Adjacent sequences: A381934 A381935 A381936 * A381938 A381939 A381940

Keyword

nonn

Author

Seiichi Manyama, Mar 10 2025

Status

approved