Geodesic
The two-parameter class of Schröder inversions
Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 1, pp. 5-19.

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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.
Classification : 05A10, 05A15, 05A19
Keywords: generalized Schröder numbers; coordination numbers; crystal ball numbers; stretched Riordan array; triangular matrix; sequence transformation; inversion; left-inverse 
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Schröder, Joachim. The two-parameter class of Schröder inversions. Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 1, pp. 5-19. http://geodesic.mathdoc.fr/item/CMUC_2013__54_1_a1/