On the Location of the Maximum Stirling Number(s) of the Second Kind

The Stirling number of the second kind S(n, k) is the number of ways of partitioning a set of n elements into k nonempty subsets. It is well known that the numbers S(n, k) are unimodal in k, and there are at most two consecutive values Kn such that (for fixed n) S(n,Kn) is maximal. We determine numerical bounds for Kn, and our result shows that in many cases Kn can be uniquely determined.