On Certain Combinatorial Expansions of the Legendre-Stirling Numbers

  • Shi-Mei Ma
  • Jun Ma
  • Yeong-Nan Yeh
Keywords: Legendre-Stirling numbers, Jacobi-Stirling numbers, Binomial coefficients


The Legendre-Stirling numbers of the second kind were introduced by Everitt et al. in the spectral theory of powers of the Legendre differential expressions. As a continuation of the work of Andrews and Littlejohn (Proc. Amer. Math. Soc., 137 (2009), 2581-2590), we provide a combinatorial code for Legendre-Stirling set partitions. As an application, we obtain expansions of the Legendre-Stirling numbers of both kinds in terms of binomial coefficients.

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