# 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} }

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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