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**
Implicit Divided Differences, Little Schröder Numbers, and Catalan Numbers
**

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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
*a*_{n} in this
formula. The main result describes six equivalent characterizations of
the sequence {*a*_{n}}.

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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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