%I #8 Aug 22 2024 09:17:22
%S 1,1,2,12,52,280,2160,16870,150080,1557360,17491600,215908000,
%T 2923905600,42734091400,672515043200,11347480544400,204142655516800,
%U 3902009862150400,78976503077472000,1687212801048174400,37941749192547200000
%N Expansion of e.g.f. exp(x^3) / (1 - x * exp(x^3/6)).
%F a(n) = n! * Sum_{k=0..floor(n/3)} ((n-3*k+6)/6)^k/k!.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^3)/(1-x*exp(x^3/6))))
%o (PARI) a(n) = n!*sum(k=0, n\3, ((n-3*k+6)/6)^k/k!);
%Y Cf. A358265, A375607, A375633.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 22 2024