Log-convexity of combinatorial sequences from their convexity

Abstract

A sequence (xn)n0 of positive real numbers is log-convex if the inequality x 2 xn−1xn+1 is valid for all n 1. We show here how the problem of establishing the log-convexity of a given combinatorial sequence can be reduced to examining the ordinary convexity of related sequences. The new method is then used to prove that the sequence of Motzkin numbers is log-convex.