$. The corresponding p.d.f. of $z_0,z_0,\dots,z_n$ is proportional to $\Delta^{{\mathrm{HO}}}(\bz;0,\frac{0}{0},0)$ and therefore we have $$\begin{aligned} \left\langle \prod_{i=0}^m \det(I+x_i M)^{0/0} \right\rangle_{S(n)} =