On the matrices related to the \(m\)-arithmetic triangle (Q1044586)

The authors introduce the \textit{\(m\)-arithmetic triangle} (\(m\geq 2\)) loosely speaking as follows: Starting with the entry \(1\) on the top of the triangle one defines the remaining entries as the sum of a particular choice of \(m\) elements from the previous row. For \(m=2\) this gives the well known triangle of binomial coefficients which is often attributed to Pascal. Any \(m\)-arithmetic triangle can be filled up with 0s to an infinite matrix which in turn gives rise to various (finite) submatrices. The aim of the present paper is to calculate determinants, factorisations and inverses of this kind of matrices.