  In this paper a formula is proved for the general degeneracy locus associated
to an oriented quiver of type A_n. Given a finite sequence of vector bundles
with maps between them, these loci are described by putting rank conditions on
arbitrary composites of the maps. Our answer is a polynomial in Chern classes
of the bundles involved, depending on the given rank conditions. It can be
expressed as a linear combination of products of Schur polynomials in the
differences of the bundles. The coefficients are interesting generalizations of
Littlewood-Richardson numbers. These polynomials specialize to give new
formulas for Schubert polynomials.
