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 A376512 #10 Sep 26 2024 03:43:01
%S A376512 1,0,2,6,12,120,480,2520,21840,120960,937440,8316000,60540480,
%T A376512 570810240,5465940480,49037788800,523588665600,5504686387200,
%U A376512 57816850291200,678823104960000,7844848544332800,93064133530368000,1184800751111577600,14967781957781452800
%N A376512 Expansion of e.g.f. exp(x^2 * (1 + x)).
%F A376512 a(n) = n! * Sum_{k=0..floor(n/2)} binomial(k,n-2*k)/k!.
%F A376512 a(n) = (n-1) * (2*a(n-2) + 3*(n-2)*a(n-3)).
%F A376512 a(n) ~ 3^(n/3 - 1/2) * exp(4/81 - 2*3^(-7/3)*n^(1/3) + 3^(-2/3)*n^(2/3) - 2*n/3) * n^(2*n/3) * (1 + 223/(3^(20/3)*n^(1/3))). - _Vaclav Kotesovec_, Sep 26 2024
%o A376512 (PARI) a(n) = n!*sum(k=0, n\2, binomial(k, n-2*k)/k!);
%Y A376512 Cf. A047974, A376513.
%Y A376512 Cf. A118589, A227937, A373740.
%K A376512 nonn,easy
%O A376512 0,3
%A A376512 _Seiichi Manyama_, Sep 25 2024