\[Z_{\kappa}\left(\mathbf{I}\right)=|\kappa|!\,2^{2|\kappa|}\,{\left[m/2\right]_%
{\kappa}}\frac{\prod\limits_{1\leq j<l\leq\ell(\kappa)}(2k_{j}-2k_{l}-j+l)}{%
\prod\limits_{j=1}^{\ell(\kappa)}(2k_{j}+\ell(\kappa)-j)!}\]