# Homework Help: Combinatorics Question

1. Nov 23, 2012

### Punkyc7

So the question was, Let x > 0.

Prove that x$^{n}$ = $\sum$ $\frac{x!}{x!-k!}$ S(n, k).

Where the sum goes from k = 1 to n and S(n, k) is th Stirling numbers.

I believe I have proven what I needed to, but my question is why does x have to be greater than 0? Couldn't we define a function that maps [n] to {-x, ......, 1}.

Last edited: Nov 23, 2012
2. Nov 23, 2012

### Ray Vickson

Is this equation accurate? The kth term blows up when x = k! for some k in {1,2,...,n}.

RGV

3. Nov 23, 2012

### Punkyc7

that should be an x! on the bottom... ill fix that