J. Integer Seq. 10(1), Article 07.1.7, 7 p., electronic only (2007)
Summary
Summary: Given a sequence $ x=\{x_n, \ n \in \mathbb{N}\}$ with integer values, or more generally with values in a ring of polynomials with integer coefficients, one can form the generalized binomial coefficients associated with $ x, {\binom nm}_x=\prod_{l=1}^{m} \frac{x_{n-l+1}}{x_l}$. In this note we introduce several sequences that possess the following remarkable feature: the fractions $ \binom nm_x$ are in fact polynomials with integer coefficients.
