  In a recent paper, Griffin, Ono and Warnaar present a framework for
Rogers-Ramanujan type identities using Hall-Littlewood polynomials to arrive at
expressions of the form \[\sum_{\lambda : \lambda_1 \leq m}
q^{a|\lambda|}P_{2\lambda}(1,q,q^2,\ldots ; q^{n}) = \text{"Infinite product
modular function"}\] for $a = 1,2$ and any positive integers $m$ and $n$. A
recent paper of Rains and Warnaar presents further Rogers-Ramanujan type
identities involving sums of terms
$q^{|\lambda|/2}P_{\lambda}(1,q,q^2,\ldots;q^n)$. It is natural to attempt to
reformulate these various identities to match the well-known Andrews-Gordon
identities they generalize. Here, we find combinatorial formulas to replace the
Hall-Littlewood polynomials and arrive at such expressions.
