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