The Euler characteristic of configuration spaces

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