Log–convexity of Combinatorial Sequences from Their Convexity

@inproceedings{Doslic2009LogconvexityOC,
title={Log–convexity of Combinatorial Sequences from Their Convexity},
author={Tomislav Doslic},
year={2009}
}

A sequence (xn)n 0 of positive real numbers is log-convex if the inequality xn 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.