On the order of Stirling numbers and alternating binomial coefficient sums (Q2765406)
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scientific article; zbMATH DE number 1694703
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the order of Stirling numbers and alternating binomial coefficient sums |
scientific article; zbMATH DE number 1694703 |
Statements
25 February 2003
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Stirling numbers of the second kind
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alternating binomial sum
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generating function
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recurrent sequence
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Fibonacci number
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Lucas number
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root of unity
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On the order of Stirling numbers and alternating binomial coefficient sums (English)
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Let \(\nu_p(r)\) denote the highest power of \(p\) that divides \(r\). The purpose of this paper is to analyze \(\nu_p (k! S(n, k))\) for an arbitrary prime \(p\), where \(S(n, k)\) denotes the Stirling numbers of the second kind. The cases \(p=3\) and \(p=5\), in particular, are treated in detail. The proofs apply, among others, properties of alternating binomial sums, recurrent sequences and roots of unity. The second author [Fibonacci Q. 32, 194-201 (1994; Zbl 0808.11017)] has previously studied the case \(p=2\).
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