I have bumped into the following expressions involving $q$-binomial coefficients. $$ \sum_{s=0}^a (-1)^s q^{s^2-s} \left(\begin{array}{c}2b+1-2s\\2a-2s\end{array}\right)_q \left(\begin{array}{c}b\\s\end{array}\right)_{q^2} $$ The expressions depend on $a$ and $b$ and are zero unless $0\leq a\leq b$.

Have these expressions appeared before? What is known about them? Any references would be appreciated.