On a Recurrence involving Stirling Numbers
Copyright policy )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 \(f(n)=(n!)^ 2(n \log 2)^{-n} n^{-1-(\log 2)/3}.\)
- Hungarian Academy of Sciences Hungary
Computational Theory and Mathematics, Fibonacci and Lucas numbers and polynomials and generalizations, Recurrences, asymptotic order of magnitude, Geometry and Topology, Stirling numbers of the second kind, Theoretical Computer Science
Computational Theory and Mathematics, Fibonacci and Lucas numbers and polynomials and generalizations, Recurrences, asymptotic order of magnitude, Geometry and Topology, Stirling numbers of the second kind, Theoretical Computer Science
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