Given two partitions M and N, with $M_i \leq N_i$ for all $1\leq i\leq \max\{l(M),l(N)\}$. Is there a formula for the generating function: $$\sum_{\lambda: M_i\leq \lambda_i\leq N_i} q^{|\lambda|}$$

I remember seeing a determinant formula before, the elements of the determinant being q-binomial coefficients. But now I can't find it.