A379084 a(n) = Sum_{k=0..floor(n/2)} binomial(2*n+k-1,k) * binomial(2*n+k,n-2*k).

1, 2, 10, 62, 394, 2562, 16966, 113794, 770458, 5254658, 36046470, 248449104, 1719175846, 11935608518, 83100064834, 579994824042, 4056746450106, 28428354905268, 199550820571858, 1402832286126650, 9875127071717694, 69599814539512900, 491081313666879968, 3468458841769675496

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = [x^n] 1/( 1/(1 + x) - x^2 )^(2*n).

a(n) == 0 (mod 2) for n>0.

Prog

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

Crossrefs

Cf. A379022, A379085.

Sequence in context: A370249 A370275 A304443 * A370626 A243034 A107026

Adjacent sequences: A379081 A379082 A379083 * A379085 A379086 A379087

Keyword

nonn

Author

Seiichi Manyama, Dec 15 2024

Status

approved