\[\sum_{\begin{subarray}{c}\pi\subseteq B(r,r,t)\\
\pi\mbox{\scriptsize\ symmetric}\end{subarray}}q^{|\pi|}=\prod_{h=1}^{r}\frac{%
1-q^{2h+t-1}}{1-q^{2h-1}}\prod_{1\leq h<j\leq r}\frac{1-q^{2(h+j+t-1)}}{1-q^{2%
(h+j-1)}}.\]