The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #22 Jun 16 2024 11:02:04
%S 1,0,1,3,3,30,105,315,2625,11340,57645,467775,2505195,17027010,
%T 142026885,922296375,7493911425,65886420600,503693415225,
%U 4625660914875,43369908657075,379618464975750,3824934458169825,38406952928819475,376103907454500225
%N Expansion of e.g.f. exp(x^2/2 * (1 + x)).
%F a(n) = n! * Sum_{k=0..floor(n/2)} binomial(k,n-2*k)/(2^k * k!).
%F a(n) = (n-1)/2 * (2*a(n-2) + 3*(n-2)*a(n-3)).
%o (PARI) a(n) = n!*sum(k=0, n\2, binomial(k, n-2*k)/(2^k*k!));
%Y Cf. A361567, A373741.
%Y Cf. A182097.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Jun 16 2024