A373855 a(n) = Sum_{k=1..n} k! * k^(n-1) * |Stirling1(n,k)|.

0, 1, 5, 80, 2690, 155074, 13658386, 1706098008, 286888266696, 62485391828448, 17112247116585744, 5755236604915060944, 2331975856351260982848, 1120439648590390138640304, 629855675998212293917375344, 409557081242059531918330384896

Offset: 0

Author

Seiichi Manyama, Jun 19 2024

Keywords

• nonn

Crossrefs

Cf. A003713, A373856.

Cf. A092552, A244585, A373857.

Cf. A320096.

Programs

Mathematica

nmax=15; Range[0,nmax]!CoefficientList[Series[Sum[(-Log[1 - k*x])^k / k,{k,nmax}],{x,0,nmax}],x] (* Stefano Spezia, Jun 19 2024 *)

PARI

a(n) = sum(k=1, n, k!*k^(n-1)*abs(stirling(n, k, 1)));

Formula

E.g.f.: Sum_{k>=1} (-log(1 - k*x))^k / k.