  Nonsymmetric interpolation Laurent polynomials in $n$ variables are
introduced, with the interpolation points depending on $q$ and on a $n$-tuple
of parameters $\tau=(\tau_1,\ldots,\tau_n)$. When $\tau_i=st^{n-i}$ Okounkov's
$3$-parameter $BC_n$-type interpolation Macdonald polynomials are recovered
from the nonsymmetric interpolation Laurent polynomials through Hecke algebra
symmetrisation with respect to a type $C_n$ Hecke algebra action. In the
appendix we give some conjectures about extra vanishing, based on Mathematica
computations in rank two.
