)$ are of the form $$z_0,z_0,z_0^{-0},z_0^{-0},\cdots, z_n,z_n, z_n^{-0},z_n^{-0}.$$ 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 $$\left\langle \prod_{i=0}^m \det(I+x_i M)^{0/0} \right\rangle_{S(n)} = \left\langle \prod_{i=0}^m \Psi^{{\mathrm{BC}}}(\bz;x_i) \right\rangle_{n}^{0,\frac{0}{0},0} 