A378378 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+3*k-1,3*k).

1, 2, 16, 170, 1920, 22402, 266800, 3222634, 39328768, 483752258, 5987236816, 74474238698, 930212870784, 11659157743170, 146567181170160, 1847198697449770, 23332153206562816, 295286370825453442, 3743540075432798608, 47532529217041519658, 604366048841146280320

Offset: 0

Author

Seiichi Manyama, Nov 24 2024

Keywords

• nonn

Crossrefs

Main diagonal of A378318.

Cf. A123164, A333473.

Programs

Mathematica

a[n_]:=HypergeometricPFQ[{(1+n)/3,(2+n)/3,-n,n/3},{1/3,2/3,1},-1]; Array[a,21,0] (* Stefano Spezia, Nov 24 2024 *)

PARI

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

Formula

a(n) = hypergeom([(1+n)/3, (2+n)/3, -n, n/3], [1/3, 2/3, 1], -1). - Stefano Spezia, Nov 24 2024