Bounds on the Location of the Maximum Stirling Numbers of the Second Kind
arXiv:0902.2964 · doi:10.1016/j.disc.2009.02.022
Abstract
Let K_n denote the smaller mode of the nth row of Stirling numbers of the second kind S(n, k). Using a probablistic argument, it is shown that for all n>=2, [exp(w(n))]-2<=K_n<=[exp(w(n))]+1, where [x] denotes the integer part of x, and w(n) is Lambert's W-function.
accepted by Discrete Mathematics