A362088 a(n) = Sum_{k=0..n} (-1)^k * binomial(-n,k) * binomial(3*k,n-k).

1, 1, 9, 55, 369, 2526, 17577, 123810, 879921, 6297643, 45325764, 327720471, 2378598885, 17319785588, 126463925310, 925620561780, 6789081127137, 49887667836693, 367189338574827, 2706613194698783, 19977334121704344, 147628150691297100

Offset

0,3

Links

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

Formula

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

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

Prog

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

Crossrefs

Column k=3 of A362078.

Cf. A362085.

Sequence in context: A183805 A037578 A096191 * A281454 A174711 A231857

Adjacent sequences: A362085 A362086 A362087 * A362089 A362090 A362091

Keyword

nonn

Author

Seiichi Manyama, Apr 08 2023

Status

approved