In this paper we give a formula for the classes (in the Grothendieck ring of complex quasi-projective varieties) of irreducible components of (1, k)-quasi-homogeneous Hilbert schemes of points on the plane. We find a new simple geometric interpretation of the q, t-Catalan numbers. Finally, we investigate a connection between (1, k)-quasi-homogeneous Hilbert schemes and homogeneous nested Hilbert schemes.is smooth and parameterizes quasi-homogeneous ideals of colength n 2010 Mathematics Subject Classification. 14C05, 05A17.