  In the the study of fractional quantum Hall states, a certain clustering
condition involving up to four integers has been identified. We give a simple
proof that particular Jack polynomials with $\alpha = - (r-1)/(k+1)$, $(r-1)$
and $(k+1)$ relatively prime, and with partition given in terms of its
frequencies by $[n_00^{(r-1)s}k 0 ^{r-1}k 0 ^{r-1}k \cdots 0 ^{r-1} m]$ satisfy
this clustering condition. Our proof makes essential use of the fact that these
Jack polynomials are translationally invariant. We also consider nonsymmetric
Jack polynomials, symmetric and nonsymmetric generalized Hermite and Laguerre
polynomials, and Macdonald polynomials from the viewpoint of the clustering.
