A374653 a(n) = Sum_{k=1..n+1} (k + 1)(n - k + 1)!.

5, 11, 27, 85, 359, 1953, 12907, 99461, 871455, 8538169, 92409683, 1094367597, 14071365511, 195177925025, 2904454929339, 46151637341653, 779850886057967, 13962610118134281, 264033196462146595, 5258262698750606909, 110001474536281307223

Offset

1,1

Links

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

Formula

a(n) = (n + 2)*hypergeom([1, 1, -n - 1], [-n - 2], 1) - (n + 1)!. - Robert Israel, Jan 08 2026

Maple

seq(simplify((n + 2)*hypergeom([1, 1, -n - 1], [-n - 2], 1) - (n + 1)!), n=1..40); # Robert Israel, Jan 08 2026

Mathematica

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

Crossrefs

Cf. A374652.

Sequence in context: A119503 A048655 A181896 * A041671 A215221 A203160

Adjacent sequences: A374650 A374651 A374652 * A374654 A374655 A374656

Keyword

nonn

Author

Clark Kimberling, Jul 25 2024

Status

approved