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 A378406 #7 Nov 25 2024 09:07:49
%S A378406 1,1,3,16,67,266,1116,4803,20707,89665,390868,1712283,7527664,
%T A378406 33196606,146800811,650724896,2890442051,12862496583,57331583055,
%U A378406 255915024714,1143845768892,5118643987872,22930389117771,102824420890590,461502269341936,2073064313021416
%N A378406 a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(n+2*k,n-2*k).
%F A378406 a(n) = [x^n] (1 + x + x^2 * (1 + x)^3)^n.
%o A378406 (PARI) a(n) = sum(k=0, n\2, binomial(n, k)*binomial(n+2*k, n-2*k));
%Y A378406 Cf. A005725, A378405.
%K A378406 nonn
%O A378406 0,3
%A A378406 _Seiichi Manyama_, Nov 25 2024