%I #7 Mar 16 2024 11:57:41
%S 1,0,2,9,52,485,4506,53137,699336,10350153,171116470,3099723341,
%T 61365024876,1315416053965,30365930429394,751142777311305,
%U 19817598092077456,555552329932290449,16489894938382046574,516644525863694081413,17038964994820269425460
%N Expansion of e.g.f. 1/(1 - x * (exp(x + x^2) - 1)).
%F a(n) = n! * Sum_{j=0..n} Sum_{k=0..j} k! * binomial(j,n-j-k) * Stirling2(j,k)/j!.
%o (PARI) a(n) = n!*sum(j=0, n, sum(k=0, j, k!*binomial(j, n-j-k)*stirling(j, k, 2)/j!));
%Y Cf. A371196, A371225.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 15 2024