Journal of Integer Sequences, Vol. 15 (2012), Article 12.6.6

Matrix Decomposition of the Unified Generalized Stirling Numbers and Inversion of the Generalized Factorial Matrices

Jiaqiang Pan
School of Biomedical Engineering and Instrumental Science
Zhejiang University
Hangzhou 210027


In this paper, we give a matrix decomposition method used to calculate unified generalized Stirling numbers in an explicit, non-recursive mode, and some of its applications. Then, we define generalized factorial matrices which may be regarded as a generalization in the form of the Vandermonde matrices, and presents some of their properties --- in particular, triangular matrix factors of the inverse matrices of the generalized factorial matrices.

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(Concerned with sequence A000032.)

Received February 15 2012; revised version received June 15 2012. Published in Journal of Integer Sequences, June 26 2012.

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