On an identity by Ercolani, Lega, and Tippings

In this note we prove that $$j!2^N\left(\genfrac{}{}{0px}{}{N+j-1}{j}\right){}_2{F}_1(\begin{array}{c}-j,-2j\\ -N-j+1\end{array};-1)=\sum _{l=0}^N\left(\genfrac{}{}{0px}{}{N}{l}\right)\prod _{i=0}^{j-1}2(2i+1+l),$$ where $N$ and $j$ are positive integers, which resolves a question posed by Ercolani, Lega, and Tippings.