A126778 Number of functions f:{1,2,...,n}->{1,2,...,n} such that Im(f) contain two fixed elements.

2, 12, 110, 1320, 19502, 341796, 6927230, 159338640, 4100173022, 116692730220, 3639243694814, 123411407978040, 4521172518708302, 177943592279325684, 7487880700093141502, 335470576863324471840, 15942605654030732807102, 801021400634789561255868

Offset: 2

Author

Aleksandar M. Janjic and Milan Janjic, Feb 18 2007

Keywords

• nonn

Links

• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Programs

Maple

a:=n->n^n-2*(n-1)^n+(n-2)^n;

Mathematica

Drop[Table[Sum[(-1)^k Binomial[2,k] (n-k)^n,{k,0,2}],{n,1,20}],1]  (* Geoffrey Critzer, Dec 23 2012 *)

Formula

a(n)=n^n-2*(n-1)^n+(n-2)^n (n=2,3,...)

Extensions

Entries checked by N. J. A. Sloane, Mar 08 2007