# Stirling numbers

• Feb 22nd 2010, 06:09 AM
bram kierkels
Stirling numbers
I want to proof

$s(n,k) = \sum_{m=k}^n{n^{m-k}s(n+1,m+1)}$

These are Stirling numbers of the first kind.
Any hints?
• Feb 22nd 2010, 07:15 AM
NonCommAlg
Quote:

Originally Posted by bram kierkels
I want to proof

$s(n,k) = \sum_{m=k}^n{n^{m-k}s(n+1,m+1)}$

These are Stirling numbers of the first kind.
Any hints?

well, it's an easy problem if you know the recurrence relation $s(n+1,m)=s(n,m-1)-ns(n,m).$ do you?
• Feb 22nd 2010, 08:52 AM
bram kierkels
Yes, i know this relation. But in a slightly different version, now i see the solution. Thanks