Factorial Stirling matrix and related combinatorial sequences Original Research Article

In this paper, some relationships between the Stirling matrix, the Vandermonde matrix, the Benoulli numbers and the Eulerian numbers are studied from a matrix representation of k!S(n,k) which will be called the factorial Stirling matrix, where S(n,k) are the Stirling numbers of the second kind. As a consequence a number of interesting and useful identities are obtained.