Combinatorial proofs of inverse relations and log-concavity for Bessel numbers

@article{Han2008CombinatorialPO,
  title={Combinatorial proofs of inverse relations and log-concavity for Bessel numbers},
  author={Hyuk Han and Seunghyun Seo},
  journal={Eur. J. Comb.},
  year={2008},
  volume={29},
  pages={1544-1554}
}
Let the Bessel number of the second kind B(n,k) be the number of set partitions of [n] into k blocks of size one or two, and let the Bessel number of the first kind b(n,k) be the coefficient of x^n^-^k in -y"n"-"1(-x), where y"n(x) is the nth Bessel polynomial. In this paper, we show that Bessel numbers satisfy two properties of Stirling numbers: The two kinds of Bessel numbers are related by inverse formulas, and both Bessel numbers of the first kind and those of the second kind form log… Expand
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