Question Number 154928 by qaz last updated on 23/Sep/21
$$\mathrm{Prove}::\:\:\:\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{m}} {\sum}}\begin{pmatrix}{\mathrm{m}}\\{\mathrm{k}}\end{pmatrix}^{\mathrm{2}} \begin{pmatrix}{\mathrm{n}+\mathrm{2m}−\mathrm{k}}\\{\:\:\:\:\:\:\mathrm{2m}}\end{pmatrix}=\begin{pmatrix}{\mathrm{m}+\mathrm{n}}\\{\:\:\:\:\mathrm{n}}\end{pmatrix}^{\mathrm{2}} \\ $$