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

1,2

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,...

Links

Robert Israel, Table of n, a(n) for n = 1..448

Formula

a(n) = (-1)^n*(n + 1)*hypergeom([1, 1, -n], [-n - 1], -1). - Robert Israel, Jan 08 2026

Maple

f:= n -> simplify((-1)^n*(n + 1)*hypergeom([1, 1, -n], [-n - 1], -1)):
map(f, [$1..40]); # Robert Israel, Jan 08 2026

Mathematica

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

Crossrefs

Cf. A000142, A014144, A374652.

Sequence in context: A370949 A002380 A274075 * A038455 A343890 A067802

Adjacent sequences: A374648 A374649 A374650 * A374652 A374653 A374654

Keyword

sign

Author

Clark Kimberling, Jul 25 2024

Status

approved