On a recurrence involving Stirling numbers
type: Item
instance of: scholarly article
title: On a recurrence involving Stirling numbers
zbMATH Open document ID: 0559.10009
DOI: 10.1016/S0195-6698(84)80035-9
author: Tamás Lengyel
published in: European Journal of Combinatorics
publication date: 1984-01-01T00:00:00Z
review text: 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 \(f(n)=(n!)^ 2(n \log 2)^{-n} n^{-1-(\log 2)/3}.\)
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11B37
zbMATH DE Number: 3891452
zbMATH Keywords: Stirling numbers of the second kind
zbMATH Keywords: asymptotic order of magnitude
reviewed by: B. M. Agrawal
MaRDI profile type: Publication
cites work: A CONVERGENCE CRITERION FOR RECURRENT SEQUENCES WITH APPLICATION TO THE PARTITION LATTICE
cites work: Asymptotic Methods in Enumeration
cites work: Q5685088
cites work: Stirling Behavior is Asymptotically Normal
cites work: Note on an Asymptotic Expansion of the $n$th Difference of Zero
cites work: On the foundations of combinatorial theory I. Theory of M�bius Functions
full work available at URL: s0195-6698(84)80035-9
OpenAlex ID: W2082454854
description: scientific article; zbMATH DE number 3891452