We introduce a rational function C _n(q, t) and conjecture that it always evaluates to a polynomial in q, t with non-negative integer coefficients summing to the familiar Catalan number \frac1n + 1( *20c 2n n )\frac{1}{{n + 1}}\left( {\begin{array}{*{20}c} {2n} \\ n \\ \end{array} } \right) . We give supporting evidence by computing the specializations D_n ( q ) = C_n ( q1 \mathord/ \vphantom 1 q q )q^{( *20c n 2 )} D_n \left( q \right) = C_n \left( {q{1 \mathord{\left/ {\vphantom {1 q}} \right. \kern-\nulldelimiterspace} q}} \right)q^{\left( {\begin{array}{*{20}c} n \\ 2 \\ \end{array} } \right)} and C _n(q) = C _n(q, 1) = C _n(1,q). We show that, in fact, D _n(q)q -counts Dyck words by the major index and C _n(q) q -counts Dyck paths by area. We also show that C _n(q, t) is the coefficient of the elementary symmetric function e _n in a symmetric polynomial DH_n(x; q, t) which is the conjectured Frobenius characteristic of the module of diagonal harmonic polynomials. On the validity of certain conjectures this yields that C _n(q, t) is the Hilbert series of the diagonal harmonic alternants. It develops that the specialization DH_n(x; q, 1) yields a novel and combinatorial way of expressing the solution of the q-Lagrange inversion problem studied by Andrews [2], Garsia [5] and Gessel [11]. Our proofs involve manipulations with the Macdonald basis {P (x; q, t)} which are best dealt with in -ring notation. In particular we derive here the -ring version of several symmetric function identities.