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# The p-adic valuation of k-central binomial coefficients

The p-adic valuation of k-central binomial coefficients
Armin Straub, Victor H. Moll, Tewodros AmdeberhanActa Arithmetica — Volume 140, Number 1, 2009, Pages 31-42

## 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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## BibTeX

@article{centralbinomials-2009,
author = {Armin Straub and Victor H. Moll and Tewodros Amdeberhan},
title = {The $p$-adic valuation of $k$-central binomial coefficients},
journal = {Acta Arithmetica},
year = {2009},
volume = {140},
number = {1},
pages = {31--42},
doi = {10.4064/aa140-1-2},
}