Integral representations of Catalan and related numbers
J. Integer Seq. 4(2), Art. 01.2.5, 6 p., electronic only (2001)
Summary
Summary: 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\dots $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.
