Generic $μ$-power ideals, fat points, and symbolic powers

Problem F of \cite{FLOS18} asks whether an ideal generated by $r$ generic $μ$-power forms, where $μ\vdash d$ is a non-pure partition, has the same Hilbert series $G_{n,d,r}=\big[(1-t^d)^r(1-t)^{-n}\big]_+$ as an ideal generated by $r$ generic forms of degree $d$. We show that the answer is negative,