# Article

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Keywords:
generalized Schröder numbers; coordination numbers; crystal ball numbers; stretched Riordan array; triangular matrix; sequence transformation; inversion; left-inverse
Summary:
Infinite lower triangular matrices of generalized Schröder 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 Schröder transformations is merged into a one-parameter class of stretched Riordan arrays, the left-inverses of which consist of matrices of crystal ball numbers. Schröder and inverse Schröder transforms of important sequences are calculated.
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