Hi everyone,

In the process of studying a problem in the Johnson association scheme I came across the following sum: $$\sum_{k\geq 0}(-1)^k\binom{n}{k}\binom{a-k}{a-b}\binom{c+k}{b}.$$ All the variables are non-negative integers. I've tried to no avail to simplify this expression using Gosper's algorithm, as well Wilf-Gosper (but it becomes unwieldy).

Is there perhaps a simpler form for this sum? Is there any connection with Eberlein polynomials?

Thanks in advance

Moshe