A sequence a0, a1, . . . , an of real numbers is said to be unimodal if for some 0 ≤ j ≤ n we have a0 ≤ a1 ≤ · · · ≤ aj ≥ aj+1 ≥ · · · ≥ an, and is said to be log-concave if a 2 i ≥ ai−1ai+1 for all 1 ≤ i ≤ n − 1. Clearly a log-concave sequence of positive terms is unimodal. The reader is referred to Stanley’s survey [10] for the surprisingly rich variety of methods to show that a sequence is l...
