An $n$-Dyck path (or a Catalan path) is a lattice path $P$, unit East and North steps, in an $n\times n$ square grid which stays (weakly) above the main diagonal. Let $\square_n$ denote all such paths. Define the **area of a path** $P$ to be the number of full squares below the path and above the diagonal. Then one variant of a $q$-Catalan number is given by
$$C_n(q)=\sum_{P\in\square_n}q^{area(P)}.$$
A few examples: $C_1(q)=1,\, C_2(q)=1+q,\, C_3(q)=1+2q+q^2+q^3$.

There is this notion of [$q,t$-Catalan numbers][1] so that $C_n(q)=C_n(q,1)$. 

I'm finding (after some fooling around) the following generating function which I've not encountered in the literature.
>**Question.** Is this known or can you provide a proof?
$$\sum_{n=0}^{\infty}C_n(q)\,z^n
=\frac{\sum_{k=0}^{\infty}q^{k^2}\prod_{j=1}^k\frac{z}{q^j-1}}
{{\sum_{k=0}^{\infty}q^{k(k-1)}\prod_{j=1}^k\frac{z}{q^j-1}}}$$


[1]: http://garsia.math.yorku.ca/MPWP/qtanalogs/catalan/