A367884 Expansion of e.g.f. 1/(1 + x * log(1-3*x)).

1, 0, 6, 27, 432, 5670, 107892, 2245320, 55380672, 1525511232, 47089609200, 1600308206640, 59508149907456, 2400782506705440, 104471929620067968, 4876509369382166880, 243046385420037166080, 12881279635221755358720, 723372722620484975659008

Offset: 0

Author

Seiichi Manyama, Dec 04 2023

Keywords

• nonn

Crossrefs

Cf. A367883.

Programs

PARI

a(n) = n!*sum(k=0, n\2, 3^(n-k)*k!*abs(stirling(n-k, k, 1))/(n-k)!);

Formula

a(0) = 1; a(n) = n! * Sum_{k=2..n} 3^(k-1)/(k-1) * a(n-k)/(n-k)!.

a(n) = n! * Sum_{k=0..floor(n/2)} 3^(n-k) * k! * |Stirling1(n-k,k)|/(n-k)!.