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Thread: Stirling numbers

  1. February 22nd 2010, 05:09 AM #1
    bram kierkels
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    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?
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  2. February 22nd 2010, 06:15 AM #2
    NonCommAlg
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    Quote Originally Posted by bram kierkels View Post
    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?
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  3. February 22nd 2010, 07:52 AM #3
    bram kierkels
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    Yes, i know this relation. But in a slightly different version, now i see the solution. Thanks
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