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.
- 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?