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[Computational Complexity] An interesting summation- new?

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  • GASARCH
    I recently came across the following sum in my research: &sumi (-1)i (k choose i)(a+i)k (Where the sum goes from i=0 to i=k.) I had reason to believe that this
    Message 1 of 1 , Jul 15, 2008
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      I recently came across the following sum in my research:

      &sumi (-1)i (k choose i)(a+i)k(Where the sum goes from i=0 to i=k.)

      I had reason to believe that this summed to (-1)kk! (which is independent of a). A mathmatician from Univ of MD, Brian Hunt, proved it for me and I wrote it up here.
      1. Is this result already known? I suspect yes but was unable to find it.
      2. I was unable to find a table of known sums on the web. Does anyone know of one?
      3. The techniques of the book A=B do not seem to apply. Does some modification of them suffice?
      4. Is there a combinatorial proof where you show that both sides solve the same problem? Is there a more elegant proof?


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      Posted By GASARCH to Computational Complexity at 7/15/2008 10:06:00 AM
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