Abstract
Homology of the group $\operatorname{Aut}(F_n)$ of automorphisms of a free group on $n$ generators is known to be independent of $n$ in a certain stable range. Using tools from homotopy theory, we prove that in this range it agrees with homology of symmetric groups. In particular we confirm the conjecture that stable rational homology of $\operatorname{Aut}(F_n)$ vanishes.