  We discuss the symmetric homogeneous polynomial solutions of the generalized
Laplace's equation which arises in the context of the Calogero-Sutherland model
on a line. The solutions are expressed as linear combinations of Jack
polynomials and the constraints on the coefficients of expansion are derived.
These constraints involve generalized binomial coefficients defined through
Jack polynomials. Generalized binomial coefficients for partitions of $k$ upto
$k=6$ are tabulated.
