A126780 Number of functions f:{1,2,...,n}->{1,2,...,n} such that Im(f) contains 4 fixed elements.

24, 360, 5880, 109200, 2298744, 54313560, 1425878520, 41215616640, 1301388272184, 44580423767880, 1647012735721080, 65286028105225200, 2764048499876532984, 124490422185142171320, 5943580498312544073720

Offset

4,1

Links

Table of n, a(n) for n=4..18.

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Formula

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

Example

a(7)=109200

Maple

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

Mathematica

Drop[Table[Sum[(-1)^k Binomial[4, k] (n-k)^n, {k, 0, 4}], {n, 1, 20}], 3]  (* Geoffrey Critzer, Dec 23 2012 *)

Crossrefs

Sequence in context: A005546 A309843 A081144 * A052741 A046905 A028115

Adjacent sequences: A126777 A126778 A126779 * A126781 A126782 A126783

Keyword

nonn

Author

Aleksandar M. Janjic and Milan Janjic, Feb 18 2007

Status

approved