Summary: We study the class \(\mathcal C\) of symmetric functions whose coefficients in the Schur basis can be described by generating functions for sets of tableaux with fixed shape. Included in this class are the Hall-Littlewood polynomials, \(k\)-Schur functions, and Stanley symmetric functions; functions whose Schur coefficients encode combinatorial, representation theoretic and geometric information. While Schur functions represent the cohomology of the Grassmannian variety of \(GL_n\), Grothendieck functions \(\{G_\lambda\}\) represent the \(K\)-theory of the same space. In this paper, we give a combinatorial description of the coefficients when any element of \(\mathcal C\) is expanded in the \(G\)-basis or the basis dual to \(\{G_\lambda\}\).