Bounds on the Location of the Maximum Stirling Numbers of the Second Kind
Abstract
Let Kn 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<=Kn<=[exp(w(n))]+1, where [x] denotes the integer part of x, and w(n) is Lambert's W-function.
0