A378378 - OEIS

%I #12 Nov 24 2024 08:31:25

%S 1,2,16,170,1920,22402,266800,3222634,39328768,483752258,5987236816,

%T 74474238698,930212870784,11659157743170,146567181170160,

%U 1847198697449770,23332153206562816,295286370825453442,3743540075432798608,47532529217041519658,604366048841146280320

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

%F a(n) = hypergeom([(1+n)/3, (2+n)/3, -n, n/3], [1/3, 2/3, 1], -1). - _Stefano Spezia_, Nov 24 2024

%t 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 *)

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

%Y Main diagonal of A378318.

%Y Cf. A123164, A333473.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 24 2024