A354752 a(n) = Sum_{k=0..n} Stirling1(n,k) * k! * n^(n-k).

1, 1, 0, 6, -152, 6670, -451152, 43685208, -5741360256, 984176280288, -213379094227200, 57100689621382176, -18489130293293779968, 7125765731670143814672, -3223822934974620319272960, 1692009521117003600170128000, -1019755541584493644326799048704

Offset: 0

Author

Ilya Gutkovskiy, Jun 06 2022

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..233

Crossrefs

Cf. A006252, A094420, A317171, A317172, A331690, A349731, A352074, A354237, A354750, A354751.

Programs

Mathematica

Unprotect[Power]; 0^0 = 1; Table[Sum[StirlingS1[n, k] k! n^(n - k), {k, 0, n}], {n, 0, 16}]
Join[{1}, Table[n! SeriesCoefficient[1/(1 - Log[1 + n x]/n), {x, 0, n}], {n, 1, 16}]]

PARI

a(n) = sum(k=0, n, stirling(n, k, 1) * k! * n^(n-k)); \\ Michel Marcus, Jun 06 2022

Formula

a(n) = n! * [x^n] 1 / (1 - log(1 + n*x) / n) for n > 0.

a(n) ~ (-1)^(n+1) * n! * n^(n-2). - Vaclav Kotesovec, Jun 06 2022