Journal of Integer Sequences, Vol. 15 (2012), Article 12.6.5

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


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}.

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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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