A possible identity popped up in a project for college, and it features q-binomial coefficient, which can be interpreted as the generating function for the number of Ferrer's boards fitting into a $k\times N-k$ box. One representation of the q-binomial is
$$\frac{(q)_N}{(q)_k (q)_{N-k}}$$
where
$$(a)_n = (1-a)(1-aq)\cdots (1-aq^{n-1})$$
Something else that pops up is
$$\frac{(aq)_N}{(aq)_k (aq)_{N-k}}$$
which looks like the q-binomial, but I can't seem to interpret it as a generating series, nor can I find reference to anything similar in literature. Any suggestions for what it might be?