The p-adic valuation of k-central binomial coefficients

Abstract

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.

arXiv comment11 pages

Cited by in corpus (2)

• Periodicity in the $p$-adic valuation of a polynomial
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