Asymptotics of the modes of the ordered Stirling numbers

Abstract

It is known that the S(n, k) Stirling numbers as well as the ordered Stirling numbers k!S(n, k) form log-concave sequences. Although in the first case there are many estimations about the mode, for the ordered Stirling numbers such estimations are not known. In this short note we study this problem and some of its generalizations.