%I #8 Dec 04 2023 06:36:11
%S 1,0,6,27,432,5670,107892,2245320,55380672,1525511232,47089609200,
%T 1600308206640,59508149907456,2400782506705440,104471929620067968,
%U 4876509369382166880,243046385420037166080,12881279635221755358720,723372722620484975659008
%N Expansion of e.g.f. 1/(1 + x * log(1-3*x)).
%F a(0) = 1; a(n) = n! * Sum_{k=2..n} 3^(k-1)/(k-1) * a(n-k)/(n-k)!.
%F a(n) = n! * Sum_{k=0..floor(n/2)} 3^(n-k) * k! * |Stirling1(n-k,k)|/(n-k)!.
%o (PARI) a(n) = n!*sum(k=0, n\2, 3^(n-k)*k!*abs(stirling(n-k, k, 1))/(n-k)!);
%Y Cf. A367883.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Dec 04 2023