Resumen de A note on a family of alternating sums of products of binomial numbers

N. Gauthier

• We study the following family of integral-valued alternating sums, where and are integers:We first consider for and non-negative integers and show that it is of the form , where may be represented as a polynomial of degree in , or expressed as a non-polynomial closed form given by a sum of binomial numbers. We then consider for a negative integer and for a non-negative integer. This reveals, in particular, that for , that for . We also show that is a polynomial of degree in , for fixed , with , and we give expressions for the coefficients.