I want to proof $\displaystyle s(n,k) = \sum_{m=k}^n{n^{m-k}s(n+1,m+1)}$ These are Stirling numbers of the first kind. Any hints?
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Originally Posted by bram kierkels I want to proof $\displaystyle s(n,k) = \sum_{m=k}^n{n^{m-k}s(n+1,m+1)}$ These are Stirling numbers of the first kind. Any hints? well, it's an easy problem if you know the recurrence relation $\displaystyle s(n+1,m)=s(n,m-1)-ns(n,m).$ do you?
Yes, i know this relation. But in a slightly different version, now i see the solution. Thanks
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