  Homology of the group 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, Aut(F_n) has no stable rational homology,
settling a conjecture of Hatcher and Vogtmann.
