Doubly Sequenced Generating Function for Binomial Coefficients

Theorem
Let $\sequence {a_{m n} }$ 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 $\sequence {a_{m n} }$ is given as:
 * $\map G {w, z} = \dfrac 1 {1 - z - w z}$