BC-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials

We consider 3-parametric polynomials which replace the A-series interpolation Macdonald polynomials in the BC case. For these polynomials, we prove: an integral representation, a combinatorial formula, Pieri-type rules, Cauchy identity, and we also show that they do not satisfy any rational q-difference equation. We also prove a binomial formula for the 6-parametric Koornwinder polynomials.