  We show that the Poincare polynomial associated with the orbifold cell
decomposition of the moduli space of smooth algebraic curves with distinct
marked points satisfies a topological recursion formula of the Eynard-Orantin
type. The recursion uniquely determines the Poincare polynomials from the
initial data. Our key discovery is that the Poincare polynomial is the Laplace
transform of the number of Grothendieck's dessins d'enfants.
