  In this short note we present a generating function computing the compactly
supported Euler characteristic $\chi_c(F(X, n), K^{\boxtimes n})$ of the
configuration spaces on a topologically stratified space $X$, with $K$ a
constructible complex of sheaves on $X$, and we obtain as a special case a
generating function for the Euler characteristic $\chi(F(X, n))$. We also
recall how to use existing results to turn our computation of the Euler
characteristic into a computation of the equivariant Euler characteristic.
