if $n\ge 1$ be postive integers,and $x,y,z$ be any real numbers,such $x+y+z=n-1$,for any real number $a$.show that
$$\dfrac{(-4)^n}{\binom{2x}{n}}\sum_{r+s=n,r,s\in Z}\dfrac{\binom{y}{r}\binom{y-a}{r}\binom{z}{s}\binom{z+a}{s}}{\binom{2y}{r}\binom{2z}{s}} =\sum_{j\ge 0}\binom{n}{2j}\dfrac{\binom{-\frac{1}{2}}{j}\binom{a-\frac{1}{2}}{j}\binom{-a-\frac{1}{2}}{j}}{\binom{x-\frac{1}{2}}{j}\binom{y-\frac{1}{2}}{j}\binom{z-\frac{1}{2}}{j}}\tag{1}$$
This problem from a book Questions left to the reader,The front problem is a polynomial treatment, the main idea is a polynomial of degree N, but in N + 1 points are zero, then this polynomial is a zero polynomial,But How to prove this identity (1)?