Recurrences for sums of powers of binomial coefficients
type: Item
instance of: scholarly article
title: Recurrences for sums of powers of binomial coefficients
zbMATH Open document ID: 0682.05006
DOI: 10.1016/0097-3165(89)90063-0
published in: Journal of Combinatorial Theory. Series A
publication date: 1989-01-01T00:00:00Z
review text: Let \(S_ n^{(r)}=\sum^{n}_{k=0}\left( \begin{matrix} n\\ k\end{matrix} \right)^ r\) \((r=1,2,...)\). An elementary method is given for finding recurrence relation for \(S_ n^{(r)}\) with \([(r+3)/2]\) terms. This confirms a conjecture of Franel. This method could easily be implemented on a computer and would require vastly less computation than Perlstadt's symbolic manipulation program MACSYMA. The recurrence relation obtained is of the type \(\sum^{k}_{j=0}b_ j^{(r)}(n)S^{(r)}_{n+1- j}=0.\) A closer examination of the proof would lead to determination of the degrees of the polynomials \(b_ j^{(r)}(n)\).
Mathematics Subject Classification ID: 05A10
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11B37
zbMATH DE Number: 4116537
zbMATH Keywords: binomial coefficients
zbMATH Keywords: recurrence relation
author: Thomas W. Cusick
describes a project that uses: MACSYMA
MaRDI profile type: Publication
full work available at URL: 0097-3165(89)90063-0
OpenAlex ID: W1970024123
cites work: Some recurrences for sums of powers of binomial coefficients
cites work: Differentiably finite power series
description: scientific article; zbMATH DE number 4116537