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

Author

Seiichi Manyama, Apr 08 2023

Keywords

• nonn

Crossrefs

Column k=3 of A362078.

Cf. A362085.

Programs

PARI

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

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.