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

• Autores: N. Gauthier
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 44, Nº. 2, 2013, págs. 253-264
• Idioma: inglés
• DOI: 10.1080/0020739x.2012.678895
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• Resumen

  • 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.