We propose formulas for the large N expansion of the generating function of connected correlators of the \(\beta \) -deformed Gaussian and Wishart–Laguerre matrix models. We show that our proposal satisfies the known transformation properties under the exchange of \(\beta \) with \(1/\beta \) and, using Virasoro constraints, we derive a recursion formula for the coefficients of the expansion. In the undeformed limit \(\beta =1\) , these coefficients are integers and they have the combinatorial interpretation of generalized Catalan numbers. For generic \(\beta \) , we define the higher genus Catalan polynomials \(C_{g,\nu }(\beta )\) whose coefficients are integer numbers.
