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 A376513 #9 Sep 26 2024 03:55:38
%S A376513 1,0,0,6,24,0,360,5040,20160,60480,1814400,19958400,99792000,
%T A376513 1037836800,21794572800,228843014400,1743565824000,29640619008000,
%U A376513 542423327846400,6082255020441600,70959641905152000,1429329929803776000,24977793950613504000
%N A376513 Expansion of e.g.f. exp(x^3 * (1 + x)).
%F A376513 a(n) = n! * Sum_{k=0..floor(n/3)} binomial(k,n-3*k)/k!.
%F A376513 a(n) = (n-1)*(n-2) * (3*a(n-3) + 4*(n-3)*a(n-4)).
%F A376513 a(n) ~ 2^(n/2 - 1) * exp(-27/1024 + 45*2^(-19/2)*n^(1/4) - 9*n^(1/2)/64 + 2^(-3/2)*n^(3/4) - 3*n/4) * n^(3*n/4) * (1 + 264471/(5*2^(37/2)*n^(1/4))). - _Vaclav Kotesovec_, Sep 26 2024
%o A376513 (PARI) a(n) = n!*sum(k=0, n\3, binomial(k, n-3*k)/k!);
%Y A376513 Cf. A047974, A376512.
%Y A376513 Cf. A373742.
%K A376513 nonn,easy
%O A376513 0,4
%A A376513 _Seiichi Manyama_, Sep 25 2024