Sequences with Inequalities

We consider infinite sequences of positive numbers. The connection between log-concavity and the Bessenrodt--Ono inequality had been in the focus of several papers. This has applications in the white noise distribution theory and combinatorics. We improve a recent result of Benfield and Roy and show that for the sequence of partition numbers \p (n) \ Nicolas' log-concavity result implies the result of Bessenrodt and Ono towards p (n) \, p (m) > p (n+m).