Implicit Divided Differences, Little Schröder Numbers, and Catalan Numbers
Georg Muntingh
Centre of Mathematics for Applications
Department of Mathematics
University of Oslo
P.O. Box 1053, Blindern
N-0316, Oslo
Norway
Abstract:
Under general conditions, the equation g(x, y) = 0 implicitly defines
y locally as a function of x. In this short note we study the
combinatorial structure underlying a recently discovered formula for
the divided differences of y expressed in terms of bivariate divided
differences of g, by analyzing the number of terms
an in this
formula. The main result describes six equivalent characterizations of
the sequence {an}.
Full version: pdf,
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(Concerned with sequences
A000108
A001003
A151374
A162326.)
Received April 12 2012;
revised version received June 12 2012.
Published in Journal of Integer Sequences, June 26 2012.
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