Product of r Choose k with r Minus Half Choose k/Formulation 1

Theorem
Let $k \in \Z$, $r \in \R$.


 * $\dbinom r k \dbinom {r - \frac 1 2} k = \dfrac {\dbinom {2 r} k \dbinom {2 r - k} k} {4^k}$

where $\dbinom r k$ denotes a binomial coefficient.