  The Getzler's formula relates the S_n-equivariant Hodge-Deligne polynomial of
the space of ordered tuples of distinct points on a given variety X with the
Hodge-Deligne polynomial of X. We obtain the analogue of this formula for the
case when X has a nontrivial automorphism group. Collecting together all strata
of $\mathcal{M}_2$ with different automorphism groups, we derive a formula for
the S_n-equivariant Euler characteristic of $\mathcal{M}_{2,n}$.
