Geodesic
Integral representations of Catalan and related numbers
Journal of integer sequences, Tome 4 (2001) no. 2
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.
Classification : 11B75, 05A10
Mots-clés : integral representations, shifted Catalan numbers, Catalan numbers, Bell numbers, inverse Mellin transform 
@article{JIS_2001__4_2_a3,
     author = {Penson,  K.A. and Sixdeniers,  J.-M.},
     title = {Integral representations of {Catalan} and related numbers},
     journal = {Journal of integer sequences},
     year = {2001},
     volume = {4},
     number = {2},
     zbl = {1004.11010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2001__4_2_a3/}
}
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%A Sixdeniers,  J.-M.
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%J Journal of integer sequences
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Penson,  K.A.; Sixdeniers,  J.-M. Integral representations of Catalan and related numbers. Journal of integer sequences, Tome 4 (2001) no. 2. http://geodesic.mathdoc.fr/item/JIS_2001__4_2_a3/