Corpus ID: 237940706

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

@inproceedings{Sprittulla2021TheOB,
  title={The ordered Bell numbers as weighted sums of odd or even Stirling numbers of the second kind},
  author={Jacob Sprittulla},
  year={2021}
}
For the Stirling numbers of the second kind S(n, k) and the ordered Bell numbers B(n), we prove the identity n/2 k=1 S(n, 2k)(2k − 1)! = B(n − 1). An analogous identity holds for the sum over odd k’s. 

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Mathematics Subject Classification: Primary 11A51; Secondary 05A17. Keywords: ordered Bell number, Stirling number of the second kind