The p-adic valuation of k-central binomial coefficients

This article by Tewodros Amdeberhan, Victor H. Moll and Armin Straub has been published in Acta Arithmetica (Volume 140, 2009, Pages 31-42) and is available at doi:10.4064/aa140-1-2.

You can also find this article on the arXiv as 0811.2028v1 [math.NT].

Abstract

The coefficients c(n,k) defined by

$$(1-k^{2}x)^{-1/k} = \sum_{n \geq 0} c(n,k)x^n$$

reduce to the central binomial coefficients $ \binom{2n}{n} $ 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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