Some Properties of Associated Stirling Numbers
Feng-Zhen Zhao
Department of Applied Mathematics
Dalian University of Technology
Dalian 116024
China
Abstract:
In this paper, we discuss the properties of associated Stirling
numbers. By means of the method of coefficients, we establish a series
of identities involving associated Stirling numbers, Bernoulli
numbers, harmonic numbers, and the Cauchy numbers of the first kind.
In addition, we give the asymptotic expansion of certain sums
involving 2-associated Stirling numbers of the second kind by
Darboux's method.
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Received December 8 2007;
revised version received May 2 2008.
Published in Journal of Integer Sequences, May 6 2008.
Minor revisions, June 11 2008; June 20 2008; July 5 2008.
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