A350726 a(n) = Sum_{k=0..n} k^(n-k) * Stirling1(n,k).

1, 1, 0, -3, 21, -100, -525, 33026, -860503, 16304464, -100885935, -12798492630, 1037135603845, -55556702499792, 2207903148318777, -31916679640973750, -6164889702150516015, 983802138243128355456, -100629406324320358067423

Offset: 0

Author

Seiichi Manyama, Feb 03 2022

Keywords

• sign

Crossrefs

Cf. A229233, A305819, A320082, A350725.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[k^(n - k) * StirlingS1[n, k], {k, 1, n}]; Array[a, 19, 0] (* Amiram Eldar, Feb 03 2022 *)

PARI

a(n) = sum(k=0, n, k^(n-k)*stirling(n, k, 1));

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, log(1+k*x)^k/(k!*k^k))))

Formula

E.g.f.: Sum_{k>=0} log(1 + k*x)^k / (k! * k^k).