Applications of Probabilistic Methods on Some Stirling Sequences
In this paper, we investigate some combinatorial sequences based on the generalized Stirling numbers and the λ-analogues of r-Stirling numbers of the first kind, then derive their moment representations in use of probabilistic methods. We also provide identities related to r-Stirling numbers of the first kind, Stirling numbers and Daehee numbers.
 G. S. Cheon, M. E. A. El-Mikkawy. Generalized harmonic numbers with Riordan arrays. J. Journal of Number Theory,128(2):413-425, 2008.
 Kim T , Kim D S . λ − analogues of r-Stirling numbers of the first kind[J].11:73-83, 2018.
 P Sun , T Wang. Probabilistic Representation with Application of Stirling Numbers. J. Journal of Mathematics,1998.
 E Lukacs. Characteristic Function. M. Charles Griffin Company Limited,London,1960.
 Chang Liu. Probability method and combinatorial identity. D. Inner Mongolia University, 2018.
Copyright (c) 2021 Journal of Progressive Research in Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.