On a class of combinatorial sums involving generalized factorials
type: Item
instance of: scholarly article
title: On a class of combinatorial sums involving generalized factorials
zbMATH Open document ID: 1142.11007
DOI: 10.1155/2007/12604
author: Elsie Sterbin Gottlieb
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2008-06-03T00:00:00Z
full work available at URL: https://eudml.org/doc/54382
review text: For the generalized falling factorial of \(t\) with increment \(\theta\) and order \(p\): \((t| \theta)_p = \prod_{j=0}^{p-1}(t-j \theta)\) \((p \geq 1)\), this paper gives a summation formula as follows: \[ \sum_{k=j}^n {k \choose j} (k + \lambda | \theta)_p = {n+1 \choose j} \sum_{r=0}^p \frac{(n+1-j)_{r+1}}{r+1+j} S(p,r;\theta,1,\lambda +j), \] where \(S(p,r;\theta,1,\lambda +j)\) are the generalized Stirling numbers.
reviewed by: Ping Sun
Mathematics Subject Classification ID: 11B73
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 5282459
zbMATH Keywords: generalized Stirling numbers
zbMATH Keywords: combinatorial sums
zbMATH Keywords: generalized factorials
MaRDI profile type: Publication
OpenAlex ID: W2069728886
cites work: Q4441313
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description: scientific article; zbMATH DE number 5282459