Some recurrences for sums of powers of binomial coefficients
type: Item
instance of: scholarly article
title: Some recurrences for sums of powers of binomial coefficients
zbMATH Open document ID: 0626.10010
DOI: 10.1016/0022-314X(87)90069-2
author: Marci A. Perlstadt
published in: Journal of Number Theory
publication date: 1987-01-01T00:00:00Z
review text: Using MACSYMA the author gives for \(r=5,6\) a recurrence relation between the terms of the sequence \(\sum^{n}_{k=0}\left( \begin{matrix} n\\ k\end{matrix} \right)^ r\). This extends earlier results with \(r=2,3,4\). Such recurrences aroused some interest several years ago in connection with Apéry's irrationality proof for \(\zeta\) (3).
reviewed by: Frits Beukers
Mathematics Subject Classification ID: 11B37
zbMATH DE Number: 4016989
zbMATH Keywords: four-term recurrences
zbMATH Keywords: sums of powers of binomial coefficients
zbMATH Keywords: MACSYMA
zbMATH Keywords: recurrence relation
describes a project that uses: MACSYMA
MaRDI profile type: Publication
cites work: Q3223132
cites work: Differentiably finite power series
cites work: A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
description: scientific article; zbMATH DE number 4016989