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Expansion of e.g.f. 1/(1 + x * log(1-3*x)).
1

%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