If I want to recursively define a function $f:\mathbb{N}\to \mathbb{N}$, I can follow the following simple schema:

1. Define f(0) explicitly.

2. For each $n\ge 0$, define $f(n+1)$ in terms of f(n).

This ensures that each natural number has a unique image under f. Now suppose I want to recursively define a two-variable function $g:\mathbb{N}\times \mathbb{N}\to \mathbb{N}$. For example, maybe I want to define binomial coefficients, or stirling numbers, or something. Is there an analogous schema I can use?

Note: I'm very new to math, so if you could be as explicit as possible, I would really appreciate it!