A068983 a(n) = Sum_{k=0..n} (k^k-k!).

0, 2, 23, 255, 3260, 49196, 867699, 17604595, 404662204, 10401033404, 295672787215, 9211294233871, 312080173805324, 11423999821072140, 449316582527563515, 18896039733447227131, 846135945932355895308, 40192537618855187742732, 2018612071634068368034711

Offset: 1

Author

Darrell Minor, Apr 02 2002

Keywords

• easy
• nonn

Comments

a(n) = number of non-injective functions [k]->[k] for 1<=k<=n.

Examples

			a(4) = 255 because (1^1-1!)+(2^2-2!)+(3^3-3!)+(4^4-4!) = 255.
		

Crossrefs

Cf. A003422, A062970, A036679.

Programs

Mathematica

Accumulate[Table[n^n-n!,{n,20}]] (* Harvey P. Dale, Aug 21 2011 *)

Formula

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

a(n) = A062970(n) - A003422(n+1). - Alois P. Heinz, Aug 10 2021