A binomial identity related to Calkin's
type: Item
instance of: scholarly article
title: A binomial identity related to Calkin's
zbMATH Open document ID: 0938.11009
DOI: 10.1016/S0012-365X(98)00178-2
author: Zhizheng Zhang
published in: Discrete Mathematics
publication date: 2000-06-12T00:00:00Z
review text: In a recent paper \textit{N. J. Calkin} [Discrete Math. 131, 335-337 (1994; Zbl 0799.05005)] had given a closed expression for the sum of the cubes of partial sums of binomial coefficients. In this note the author considers the sum of the same terms, but with alternative signs, i.e. he shows for an odd number \(n\) \[ \sum_{s=0}^{n}(-1)^s \left(\sum_{k=0}^s {n\choose k}\right)^3 = -n2^{3n-1}-3(-1)^{(n-1)/2}2^{n-1}{n-1 \choose (n-1)/2}. \] (Remark. Obviously, the formula in Theorem 2 contains a misprint, instead of \(s\) please read \(k\)).
reviewed by: Helmut Müller
Mathematics Subject Classification ID: 11B65
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 05A10
zbMATH DE Number: 1321784
zbMATH Keywords: binomial sums
MaRDI profile type: Publication
cites work: A curious binomial identity
Wikidata QID: Q127359271
description: scientific article; zbMATH DE number 1321784