Let $B_n$ denote the group of signed permutations on $n$ letters. Is there a good explanation or understandable way to see why $$ \sum_{w\in B_n}q^{\text{inv}(w)}=(2n)_q(2n-2)_q\cdots(2)_q? $$
I've been thinking about it on and off while reading through Taylor's Geometry of the Classical Groups, but don't understand why this identity holds. I appreciate any explanation. Thanks!