On a recurrence involving Stirling numbers
Let \(Z(n)=\sum^{n-1}_{k=1}S(n,k) Z(k)\), where S(n,k) denotes the Stirling numbers of the second kind. The author proves the asymptotic order of magnitude of Z(n), i.e. \(c_ 1\leq Z(n)/f(n)\leq c_ 2\) where \(c_ 1\), \(c_ 2\) are positive constants, and \(f(n)=(n!)^ 2(n \log 2)^{-n} n^{-1-(\log 2)/3}.\)
scientific article; zbMATH DE number 3891452