On the location of the maximum Stirling number(s) of the second kind (Q732762)

The Stirling number of the second kind, \(S(n,k)\), is the number of partitions of an \(n\)-element set into \(k\) nonempty subsets. It has been known that sequence is unimodal in \(k\) and asymptotically normal. Unimodality implies that for fixed \(n\), one or two consecutive values of \(k\) realize \(\max_k S(n,k)\). The paper gives an explicit interval that includes the (first) \(k\) realizing the maximum -- i.e. no \(O(\,)\) notation is involved. (It is not known whether the maximum value can occur twice for any \(n\geq 3\).)