On a connection between the Pascal, Vandermonde and Stirling matrices-II

摘要

This article is an extension of the work presented in [On a connection between the Pascal, Vandermonde and Stirling matrices-I, Applied Mathematics and Computation, 2003, to appear]. It gives a full matrix T(t) for which T(1) is exactly the lower triangular stochastic matrix T given in [On a connection between the Pascal, Vandermonde and Stirling matrices-I, Applied Mathematics and Computation, 2003, to appear]. A new strategy to generate the elements of the matrix T=T(1) is investigated. A new conjecture and three combinatorial identities are also given.