Fuss–Catalan Matrices, Their Weighted Sums, and Stabilizer Subgroups of the Riordan Group

In this paper, we present the Riordan arrays called Fuss–Catalan matrices which are constructed by the convolutions of the generating functions of the Fuss–Catalan numbers. We also discuss weighted sums of the Fuss–Catalan matrices, using such matrices as transformations of recursive sequences, and their connection with stabilizer subgroups of the Riordan group.