(0n)} =  \left\langle \prod_{i=0}^m \Psi^{{\mathrm{BC}}}(\bz;x_i) \right\rangle_{n}^{0,0,0} = \prod_{i=0}^m x_i^n \cdot  P_{(n^m)}^{{\mathrm{HO}}}(x_0,\dots,x_m;0,0,0).$$ Here $P_\lambda^{{\mathrm{HO}}}(x_0,\dots,x_m;0,0,0)$ is just the irreducible character of $S