A354674 - OEIS

%I #8 Jun 02 2022 15:38:26

%S 1,1,33,4568,1653010,1236180194,1657339714418,3620923498508952,

%T 12037504737979759944,57827877567223173191712,

%U 385581993722741959459382352,3454851578510897594456017095504,40509304222426523176427339597382336

%N a(n) = Sum_{k=0..n} k! * k^(k+n) * |Stirling1(n,k)|.

%F E.g.f.: Sum_{k>=0} (-k * log(1 - k*x))^k.

%o (PARI) a(n) = sum(k=0, n, k!*k^(k+n)*abs(stirling(n, k, 1)));

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-k*log(1-k*x))^k)))

%Y Cf. A320096, A350721, A350722, A351333, A351769.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jun 02 2022