Note on the outdegree of a node in random recursive trees (Q1429335)

A tree \(T_n\) with \(n\) labelled nodes, rooted at node 1, is a recursive tree if the labels of the nodes encountered in any path leading away from the root form an increasing sequence; there are \((n-1)!\) such trees. The authors derive an expression, in terms of the Stirling numbers of the first kind, for the probability that node \(i\) in such a tree has out-degree \(k\).