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arXiv · 0811.2028

The p-adic valuation of k-central binomial coefficients

Armin Straub·Tewodros Amdeberhan·Victor H. Moll
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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.

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Armin Straub, Tewodros Amdeberhan, Victor H. Moll. 2008-11-13. The p-adic valuation of k-central binomial coefficients. https://doi.org/10.4064/aa140-1-2

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