A374651 a(n) = Sum_{k=1..n+1} (-1)^(k-1) k (n - k + 1)!.

-1, 3, 1, 19, 81, 539, 3881, 32019, 294961, 3006859, 33608121, 408778499, 5375855681, 76017801339, 1150262909641, 18546246267379, 317444672651601, 5748938114157419, 109829779507865561, 2207493511046751459, 46566125370108071521, 1028660983526344785499

Offset: 1

Author

Clark Kimberling, Jul 25 2024

Keywords

• sign

Comments

Residues mod 10 are 9,3,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,...

Crossrefs

Cf. A000142, A014144, A374652.

Programs

Mathematica

t[n_] := Sum[(-1)^(k - 1) k*(n - k + 1)!, {k, 1, n + 1}]
Table[t[n], {n, 1, 30}]