Totally symmetric singlets for 2 or (2n_ir-2) electrons

n = 2         a = 0        b = - n_ir

$${\frac{{n_{ir}(n_{ir}-2)}}{{(n_{ir}-1)^2}}}$$ n = (2n_ir - 2)         a

$${\frac{{n_{ir}(n_{ir}-3)}}{{(n_{ir}-1)^2}}}$$ b

This covers the ¹S states of p², p⁴, d², d⁸, etc.