We will discuss counting of orientable and nonorientable gluings of regular 2n-gons using gaussian matrix integrals. <...> Key words and phrases: matrix integrals, generalized Catalan numbers, generating function of gluings, virtual Euler characteristic. 1. <...> Contribution (for example, the partition function) of each chart is included with the factor N in the degree of the Euler characteristic of the surface on which you can draw graphs. <...> As is well known, in the main (or planar) approximation of N in the gaussian First time a gaussian matrix model was proposed by E.Wigner to describe the hermitian matrix model the correlation functions are the Catalan numbers. <...> At the same time, the number for ways of gluings 2n-gon to get the sphere, too, will give the nth Catalan number. <...> Moreover, J.Harer and D.Zagier [2–4] was found the generating function for the number for orientable gluings of all sorts. <...> The number of gluings 2n-gon, giving a surface of genus g, can be regarded as generalized Catalan numbers 𝜖g(n). <...> These numbers were obtained by the recurrence relations. <...> Correlations in this model are even or odd polynomials of degree N. For odd n, we obtain a polynomial of even degree and vice versa. <...> By the way, the main achievement of [2] is even more interesting result, namely the computation of virtual Euler characteristic of the moduli space for the two-dimensional surface of genus g with n marked points. <...> They are described by gaussian integrals on symmetric matrices. <...> We will present examples of calculations for correlators in this model. <...> They already have the form of polynomials in N with non-zero coefficients for all the terms of the lowest degrees. 2. <...> Orientable Case At first the generating function for orientable gluings of regular 2n-gons was obtained by Harer and Zagier [2]. <...> Shishanin A. O. Matrix Integrals and Gluings of Regular 2n-gons 285 It is possible to count the number of orientable gluings using gaussian hermitian matrix model. <...> Let us define a sequence of polynomials Tn(N) = ∑ g=0 𝜖g(n)Nn+1−2g = ∑ g=0 where χ(g) is Euler characteristic. <...> B. Lass [8] obtained pure combinatorial proof of the formula <...>