【Abstract】 The generalized Motzkin numbers unify many well-known counting coefficients, such as the Bell numbers, the Catalan numbers, the Motzkin numbers, the central binomial coefficients, the large and little Schroeder numbers. In this talk we discuss various combinatorial properties of the generalized Motzkin numbers, including lattice path interpretations, recurrence relations, and Hankel transforms. We also discuss the log-convexity and moment properties of such numbers.
