%I #8 Aug 29 2024 11:24:35
%S 1,1,2,6,36,240,1800,16800,178080,2086560,27518400,399168000,
%T 6286896000,107623676160,1984274772480,39143052748800,824445099878400,
%U 18450791322163200,437015358530150400,10929450232744243200,287728555881102336000,7952251084537503744000
%N Expansion of e.g.f. 1/(1 + (log(1 - x^3))/x^2).
%F a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k)! * |Stirling1(n-2*k,n-3*k)|/(n-2*k)!.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x^3)/x^2)))
%o (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)!*abs(stirling(n-2*k, n-3*k, 1))/(n-2*k)!);
%Y Cf. A007840, A375798.
%Y Cf. A353223.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 29 2024