A206816 a(n) = Sum_{0

1, 9, 63, 447, 3447, 29367, 276327, 2856807, 32250087, 395130087, 5225062887, 74201293287, 1126567808487, 18213512883687, 312440245683687, 5668674457011687, 108462341176755687, 2182831421832627687, 46096712669420979687

Offset: 2

Author

Clark Kimberling, Feb 12 2012

Keywords

• nonn

Examples

			a(4) = (24-1) + (24-2) + (24-6) = 63.
		

Links

• Danny Rorabaugh, Table of n, a(n) for n = 2..400

Crossrefs

Cf. A000142, A206817, A001563, A007489.

Programs

Maple

seq(add(k^2*k!,k=1..n-1), n=2..30); # Ridouane Oudra, Jun 13 2025

Mathematica

s[k_] := k!; t[1] = 0;
p[n_] := Sum[s[k], {k, 1, n}];
c[n_] := n*s[n] - p[n];
t[n_] := t[n - 1] + (n - 1) s[n] - p[n - 1];
Table[c[n], {n, 2, 32}]           (* A206816 *)
Flatten[Table[t[n], {n, 2, 20}]]  (* A206817 *)

PARI

a(n) = sum(j=1, n-1, n!-j!); \\ Michel Marcus, Jun 13 2025

Sage

[sum([factorial(n)-factorial(j) for j in range(1,n)]) for n in range(2,21)] # Danny Rorabaugh, Apr 18 2015

Formula

a(n) = n*n!-p(n), where p(n) is the n-th partial sum of (j!).

a(n) = t(n)-t(n-1), where t = A206817.

a(n) = Sum_{k=1..n-1} k^2*k!. - Ridouane Oudra, Jun 13 2025

a(n) = A001563(n) - A007489(n). - Ridouane Oudra, Jun 14 2025