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