  In the case of Dynkin quivers we establish a formula for the Grothendieck
class of a quiver cycle as the iterated residue of a certain rational function,
for which we provide an explicit combinatorial construction. Moreover, we
utilize a new definition of the double stable Grothendieck polynomials due to
Rimanyi and Szenes in terms of iterated residues to exhibit how the computation
of quiver coefficients can be reduced to computing coefficients in Laurent
expansions of certain rational functions.
