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

  title={The \$p\$-adic valuation of \$k\$-central binomial coefficients},
  author={Armin Straub and Tewodros Amdeberhan and Victor H. Moll},
  journal={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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