  In this article we give a combinatorial formula for a certain class of
Koornwinder polynomials, also known as Macdonald polynomials of type
$\tilde{C}$. In particular, we give a combinatorial formula for the Koornwinder
polynomials $K_{\lambda} = K_{\lambda}(z_1,\dots,z_N; a,b,c,d; q,t)$, where
$\lambda = (1,\dots,1,0,\dots,0)$. We also give combinatorial formulas for all
``open boundary ASEP polynomials'' $F_{\mu}$, where $\mu$ is a composition in
$\{-1,0,1\}^N$; these polynomials are related to the nonsymmetric Koornwinder
polynomials $E_{\mu}$ up to a triangular change of basis. Our formulas are in
terms of rhombic staircase tableaux, certain tableaux that we introduced in
previous work to give a formula for the stationary distribution of the
two-species asymmetric simple exclusion process (ASEP) on a line with open
boundaries.
