Geodesic
Deformations of the Taylor formula
Journal of integer sequences, Tome 10 (2007) no. 1.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 05A10, 05A30, 11B39, 11B65
Keywords: generalized binomial coefficients 
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Ferrand, Emmanuel. Deformations of the Taylor formula. Journal of integer sequences, Tome 10 (2007) no. 1. http://geodesic.mathdoc.fr/item/JIS_2007__10_1_a2/