I have a sequence of ordered pairs: $$(0,1), (0,2), (0,3), (0,4), \ldots, (0, n),$$ $$(1,2), (1,3), (1,4), \ldots, (1, n),$$ $$(2,3), (2,4), \ldots, (2, n),$$ $$(3,4), \ldots, (3, n),$$ $$\ldots,$$ $$(m,n),$$ where $m<n$ $\forall m, n \in \mathbb{N}_0$ and the maximal value of $m$ equals $n-1$.
Question. How to write down this sequence with the set notation?
Edit. My attempt is: $A=\{(m,n): m<n, max(m)=n-1, m,n \in \mathbb{N}_0 \}$.