The ordered Bell numbers as weighted sums of odd or even Stirling numbers of the second kind

2021/09/26 by Jacob Sprittulla, Sprittulla, Jacob
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.2109.12705

openalex publication_date 2021/09/26 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28

Abstract

For the Stirling numbers of the second kind S(n,k) and the ordered Bell numbers B(n), we prove the identity ∑_k=1^n/2 S(n,2k)(2k-1)! = B(n-1). An analogous identity holds for the sum over odd k's.

Citations

• The on-line encyclopedia of integer sequences

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