Value of finite sum

1. Jan 18, 2008

Pere Callahan

Hi,

I came across a somewhat unwieldy sum which I do not know how to manipulate any further. I suspect it might have something to do with a hypergeometric series, but I am not sufficiently familar with those series to be able to just see how it might be related to them.

The sum in question is

$$\sum_{1\leq r_1< r_2 < \dots < r_n \leq m}{\frac{ (k-1)!!(k-2r_1)!!(k-2r_2+1)!! \dots (k-2r_{n-1}+n-2)!!(k-2r_n+n-1)!! }{ (k-2r_1+1)!!(k-2r_2+2)!! \dots (k-2r_{n-1}+n-1)!!(k-2r_n+n)!! }}$$

where k is some non-negative integer, $$0\leq n \leq k$$. m is defined by

$$m=\left\lfloor\frac{k+n}{2}\right\rfloor \geq n$$.

Do you know of any books where I could look up things like that?

Any help is greatly appreciated.

-Pere

Last edited: Jan 18, 2008
2. Jan 19, 2008

CRGreathouse

3. Jan 26, 2008

Pere Callahan

Thanks. A=B seems to be an intersting book, I hadn't heard of it before.