A351796 a(n) = n! * Sum_{k=0..n} (-k * (n-k))^k/k!.

1, 1, 0, 6, 36, -1240, 36810, -743568, -4441640, 2126086272, -201265464330, 13670088101120, -512174277963612, -50655591400627200, 16935777106057251442, -2936123018591228282880, 368896773292405165345200, -22278163772113766968557568

Offset: 0

Author

Seiichi Manyama, Feb 19 2022

Keywords

• sign

Crossrefs

Cf. A351780, A351795.

Programs

Mathematica

a[n_] := n!*(1 + Sum[(-k*(n - k))^k/k!, {k, 1, n}]); Array[a, 18, 0] (* Amiram Eldar, Feb 19 2022 *)

PARI

a(n) = n!*sum(k=0, n, (-k*(n-k))^k/k!);