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 A375629 #8 Aug 22 2024 09:16:36
%S A375629 1,2,6,26,148,1052,8974,89294,1015480,12991832,184682554,2887850858,
%T A375629 49261993444,910356170804,18117379906630,386315966673638,
%U A375629 8786555389140976,212335975835710256,5433155029435593970,146744457899073450050,4172032796528725318876
%N A375629 Expansion of e.g.f. exp(2*x) / (1 - x^2 * exp(x)).
%F A375629 a(n) = n! * Sum_{k=0..floor(n/2)} (k+2)^(n-2*k)/(n-2*k)!.
%o A375629 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x)/(1-x^2*exp(x))))
%o A375629 (PARI) a(n) = n!*sum(k=0, n\2, (k+2)^(n-2*k)/(n-2*k)!);
%Y A375629 Cf. A368265, A375630.
%Y A375629 Cf. A358080.
%K A375629 nonn
%O A375629 0,2
%A A375629 _Seiichi Manyama_, Aug 21 2024