This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A378378 #12 Nov 24 2024 08:31:25
%S A378378 1,2,16,170,1920,22402,266800,3222634,39328768,483752258,5987236816,
%T A378378 74474238698,930212870784,11659157743170,146567181170160,
%U A378378 1847198697449770,23332153206562816,295286370825453442,3743540075432798608,47532529217041519658,604366048841146280320
%N A378378 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+3*k-1,3*k).
%F A378378 a(n) = hypergeom([(1+n)/3, (2+n)/3, -n, n/3], [1/3, 2/3, 1], -1). - _Stefano Spezia_, Nov 24 2024
%t A378378 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 A378378 (PARI) a(n) = sum(k=0, n, binomial(n, k)*binomial(n+3*k-1, 3*k));
%Y A378378 Main diagonal of A378318.
%Y A378378 Cf. A123164, A333473.
%K A378378 nonn
%O A378378 0,2
%A A378378 _Seiichi Manyama_, Nov 24 2024