The p-adic valuation of k-central binomial coefficients

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2009Embargo end date: 01 Jan 2008 English Publisher:Institute of Mathematics, Polish Academy of SciencesJournal:Acta Arithmetica, volume 140, pages 31-42 (issn: 0065-1036, eissn: 1730-6264,

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Authors: Straub, Armin; Amdeberhan, Tewodros; Moll, Victor H.;

doi: 10.4064/aa140-1-2 , 10.48550/arxiv.0811.2028

arXiv: 0811.2028

The p-adic valuation of k-central binomial coefficients

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Abstract

The coefficients c(n,k) defined by (1-k^2x)^(-1/k) = sum c(n,k) x^n reduce to the central binomial coefficients for k=2. Motivated by a question of H. Montgomery and H. Shapiro for the case k=3, we prove that c(n,k) are integers and study their divisibility properties.

11 pages

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Keywords

Mathematics - Number Theory, 11A51, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO)

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