  Grothendieck polynomials were introduced by Lascoux and Sch\"utzenberger, and
they play an important role in K-theoretic Schubert calculus. In this paper, we
give a new definition of double stable Grothendieck polynomials based on an
iterated residue operation. We illustrate the power of our definition by
calculating the Grothendieck expansion of K-theoretic Thom polynomials of $A_2$
singularities. We present the expansion in two versions: one displays its
expected stabilization, while the other displays its expected finiteness
property.
