A379086 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(3*n+k,n-2*k).

1, 3, 21, 174, 1509, 13443, 121962, 1120899, 10401021, 97230090, 914283621, 8638552464, 81945757734, 779949538176, 7444735446813, 71237074583589, 683125330952205, 6563268117869076, 63164380112090814, 608805362150884731, 5875874727915635409, 56780302474503539427, 549294315060885105744

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = [x^n] 1/( 1/(1 + x) - x^2 )^(3*n).

a(n) == 0 (mod 3) for n>0.

Prog

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

Crossrefs

Cf. A379025, A379087.

Cf. A379088.

Sequence in context: A365136 A228923 A287995 * A257675 A372108 A195105

Adjacent sequences: A379083 A379084 A379085 * A379087 A379088 A379089

Keyword

nonn

Author

Seiichi Manyama, Dec 15 2024

Status

approved