|Journal of Integer Sequences, Vol. 4 (2001), Article 01.2.5|
Université Pierre et Marie Curie
Laboratoire de Physique Théorique des Liquides
Tour 16, 5 étage, 4 place Jussieu
75252 Paris Cedex 05, France
Email addresses: email@example.com and firstname.lastname@example.org
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.
(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.