Faber's intersection number conjecture in $\psi$-form

Let ${\mathcal M}_{g,n}^{rt}$ be the moduli space of stable $n$-pointed genus-$g$ curves with rational tails, and let

$$\pi:{\mathcal M}_{g,n}^{rt}\longrightarrow {\mathcal M}_{g,1}$$

be the forgetful morphism. For positive integers $d_1,\ldots,d_n$, write $(2a-1)!!=1\cdot3\cdots(2a-1)=(2a)!/(2^a a!)$. Faber's intersection number conjecture. For every $n$-tuple of positive integers $(d_1,\ldots,d_n)$ satisfying $\sum_i d_i=g-2+n$, one has

$$\pi_*\left(\psi_1^{d_1}\cdots\psi_n^{d_n}\right)=\frac{(2g-3+n)!(2g-1)!!}{(2g-1)!\prod_{j=1}^n(2d_j-1)!!}\,\psi_1^{g-1}.$$

This is a proposed explicit formula for tautological intersection classes on the rational-tails locus and is the $\psi$-class form of Faber's intersection number conjecture. The supplied text does not establish its resolution.