Journal of Integer Sequences, Vol. 4 (2001), Article 01.2.5

Integral Representations of Catalan and Related Numbers

K. A. Penson and J.-M. Sixdeniers

Université Pierre et Marie Curie
Laboratoire de Physique Théorique des Liquides
Tour 16, 5 étage, 4 place Jussieu
75252 Paris Cedex 05, France

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Abstract: We derive integral representations for the Catalan numbers C(n), shifted Catalan numbers C(n+p), and the numbers n!*C(n) and C(n)*B(n), where B(n) are the Bell numbers, for n=0,1... Our method is to use inverse Mellin transform. All these numbers are power moments of positive functions, and their representations turn out to be unique.

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(Concerned with sequences A000108, A000110, A001761, A060593, A064299 .)

Received September 7, 2001; revised version received October 29, 2001. Published in Journal of Integer Sequences, February 7, 2002.

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