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

@article{Straub2009TheV,
title={The \$p\$-adic valuation of \$k\$-central binomial coefficients},
author={Armin Straub and Tewodros Amdeberhan and Victor H. Moll},
journal={Acta Arithmetica},
year={2009},
volume={140},
pages={31-42}
}
• Published 13 November 2008
• Mathematics
• Acta Arithmetica
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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