A126781 Number of functions f:{1,2,...,n}->{1,2,...,n} such that Im(f) contains 6 fixed elements.

720, 20160, 514080, 13608000, 385363440, 11760819840, 386860668480, 13682898028800, 518666099711760, 20997894426949440, 904827327153291360, 41367795437773022400, 2000634709955550047280, 102066613831917982920960

Offset: 6

Author

Aleksandar M. Janjic and Milan Janjic, Feb 18 2007

Keywords

• nonn

Examples

			a(7)=20160
		

Links

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

Crossrefs

Cf. A039621 (Lehmer-Comtet numbers of 2nd kind).

Programs

Maple

a:=n->n^n-6*(n-1)^n+15*(n-2)^n-20*(n-3)^n+15*(n-4)^n-6*(n-5)^n+(n-6)^n;

Mathematica

Drop[Table[Sum[(-1)^k Binomial[6,k] (n-k)^n,{k,0,6}],{n,1,20}],5]  (* Geoffrey Critzer, Dec 23 2012 *)

Formula

a(n)=n^n-6*(n-1)^n+15*(n-2)^n-20*(n-3)^n+15*(n-4)^n-6*(n-5)^n+(n-6)^n, (n=6,7,...)