I recently came across the following sum in my research:
&sum
_{i} (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)
^{k}k!
(which is independent of a).
A mathmatician from Univ of MD,
Brian Hunt,
proved it for me and I wrote it up
here.

Is this result already known? I suspect yes but was unable to find it.

I was unable to find a table of known sums on the web. Does anyone know of one?

The techniques of the book
A=B
do not seem to apply. Does some modification of them suffice?

Is there a combinatorial proof where you show that both sides solve
the same problem? Is there a more elegant proof?

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