Geodesic
Deformations of the Taylor formula
Journal of integer sequences, Tome 10 (2007) no. 1
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 
@article{JIS_2007__10_1_a2,
     author = {Ferrand,  Emmanuel},
     title = {Deformations of the {Taylor} formula},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {1},
     zbl = {1114.05004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_1_a2/}
}
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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/