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 A375652 #10 Aug 23 2024 02:11:54
%S A375652 1,2,6,26,136,812,5494,41414,341800,3056984,29415274,302501498,
%T A375652 3305797444,38212967444,465409979038,5951991056558,79686155008816,
%U A375652 1113909729606896,16219814971477330,245503998889083362,3855373914424695196,62708526467241370892
%N A375652 Expansion of e.g.f. exp(2*x + x^2 * exp(x)).
%F A375652 a(n) = n! * Sum_{k=0..floor(n/2)} (k+2)^(n-2*k) / (k! * (n-2*k)!).
%o A375652 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x+x^2*exp(x))))
%o A375652 (PARI) a(n) = n!*sum(k=0, n\2, (k+2)^(n-2*k)/(k!*(n-2*k)!));
%Y A375652 Cf. A216507, A375651.
%Y A375652 Cf. A367874, A375629.
%K A375652 nonn
%O A375652 0,2
%A A375652 _Seiichi Manyama_, Aug 22 2024