Journal of Integer Sequences, Vol. 16 (2013), Article 13.3.6

Congruence Classes of 2-adic Valuations of Stirling Numbers of the Second Kind

Curtis Bennett and Edward Mosteig
Department of Mathematics
Loyola Marymount University
Los Angeles, CA 90045


We analyze congruence classes of S(n,k), the Stirling numbers of the second kind, modulo powers of 2. This analysis provides insight into a conjecture posed by Amdeberhan, Manna and Moll, which those authors established for k at most 5. We provide a framework that can be used to justify the conjecture by computational means, which we then complete for values of k between 5 and 20.

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Received April 27 2012; revised version received February 17 2013. Published in Journal of Integer Sequences, March 2 2013.

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