Abstract:Infinite lower triangular matrices of generalized Schr\"oder numbers are used to construct a two-parameter class of invertible sequence transformations. Their inverses are given by triangular matrices of coordination numbers. The two-parameter class of Schr\"oder transformations is merged into a one-parameter class of stretched Riordan arrays, the left-inverses of which consist of matrices of crystal ball numbers. Schr\"oder and inverse Schr\"oder transforms of important sequences are calculated.
Keywords: generalized Schr\"oder numbers, coordination numbers, crystal ball numbers, stretched Riordan array, triangular matrix, sequence transformation, inversion, left-inverse
AMS Subject Classification: 05A10 05A15 05A19