## Joachim SchrÃ¶der

*The two-parameter class of Schr\"oder inversions*

Comment.Math.Univ.Carolin. 54,1 (2013) 5-19.**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

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