If you are asking
what that series is equal to i think its
This what I got in terms of a summation.
hes right I did not see the alternating signs
I suppose that the answer should be given in a closed form. I can see that it can be written shorter using the sum symbol ( )...
That happens to count the number of surjections from a set of k to a set of k objects.
Originally Posted by james_bond
Or another way it counts surjections from a finite set of k objects onto itself. Those happen to be permutations.
How ways can we permute k objects. That is your answer.