Doubly Sequenced Generating Function for Binomial Coefficients

Theorem
Let $\left \langle {a_{m n} }\right \rangle$ be the doubly subscripted sequence defined as:
 * $\forall m, n \in \N_{\ge 0}: a_{m n} = \dbinom n m$

where $\dbinom n m$ denotes a binomial coefficient.

Then the generating function for $\left \langle {a_{m n} }\right \rangle$ is given as:
 * $G \left({w, z}\right) = \dfrac 1 {1 - z - w z}$