On a connection between the Pascal, Vandermonde and Stirling matrices––I

摘要

In the current paper the author investigates a connection between the Pascal, Vandermonde and Stirling matrices where each of them is of size n by n. Computer-aided study using MAPLE shows that a new stochastic matrix links together these matrices. This stochastic matrix together with its multiplicative inverse are presented for the case n=10. Some combinatorial identities are also given.