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 A378407 #5 Nov 25 2024 09:07:54
%S A378407 1,1,1,4,25,106,352,1114,3865,14539,54886,201763,732568,2679535,
%T A378407 9917818,36903049,137265337,510201961,1898730307,7082472358,
%U A378407 26468394430,99026247688,370771000975,1389387381691,5211329801272,19564292736706,73504888190371,276350941918741
%N A378407 a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(n+2*k,n-3*k).
%F A378407 a(n) = [x^n] (1 + x + x^3 * (1 + x)^3)^n.
%o A378407 (PARI) a(n) = sum(k=0, n\3, binomial(n, k)*binomial(n+2*k, n-3*k));
%Y A378407 Cf. A228960.
%K A378407 nonn
%O A378407 0,4
%A A378407 _Seiichi Manyama_, Nov 25 2024