On a recurrence involving Stirling numbers (Q802590)
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scientific article; zbMATH DE number 3891452
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a recurrence involving Stirling numbers |
scientific article; zbMATH DE number 3891452 |
Statements
On a recurrence involving Stirling numbers (English)
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1984
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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 \(f(n)=(n!)^ 2(n \log 2)^{-n} n^{-1-(\log 2)/3}.\)
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Stirling numbers of the second kind
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asymptotic order of magnitude
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