Symmetric polynomials are the invariants of the classical action of the symmetric group Sn on the space Q[Xn] of polynomials by permutation of the variables. It is well known that the dimension of the quotient of Q[Xn] by the ideal generated by symmetric, constant-free polynomials is n!. When we consider other actions or other groups, we have different spaces of invariants, and different quotients (coinvariants). We will discuss some examples, in particular quasi-symmetrizing actions, whose coinvariants have dimensions given by the Catalan numbers. We shall give explicit Grobner bases for the ideals generated by the invariants .