Log–convexity of Combinatorial Sequences from Their Convexity

  title={Log–convexity of Combinatorial Sequences from Their Convexity},
  author={Tomislav Doslic},
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. 

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