\[\genfrac{(}{)}{0.0pt}{}{z}{k}=\frac{z(z-1)\cdots(z-k+1)}{k!}=\frac{(-1)^{k}{%
\left(-z\right)_{k}}}{k!}=(-1)^{k}\genfrac{(}{)}{0.0pt}{}{k-z-1}{k}.\]