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 A375631 #8 Aug 22 2024 09:17:09
%S A375631 1,2,5,17,76,422,2809,21821,193708,1934468,21465529,262007033,
%T A375631 3488768650,50326173458,781808322481,13012772925293,231029881905736,
%U A375631 4358082011900744,87045479653871377,1835177785479753545,40727378713879346206,949039029924830652662
%N A375631 Expansion of e.g.f. exp(2*x) / (1 - x^2/2 * exp(x)).
%F A375631 a(n) = n! * Sum_{k=0..floor(n/2)} (k+2)^(n-2*k)/(2^k*(n-2*k)!).
%o A375631 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x)/(1-x^2/2*exp(x))))
%o A375631 (PARI) a(n) = n!*sum(k=0, n\2, (k+2)^(n-2*k)/(2^k*(n-2*k)!));
%Y A375631 Cf. A368265, A375632.
%K A375631 nonn
%O A375631 0,2
%A A375631 _Seiichi Manyama_, Aug 21 2024