Geodesic
A common generating function for Catalan numbers and other integer sequences
Journal of integer sequences, Tome 6 (2003) no. 1.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Catalan numbers and other integer sequences (such as the triangular numbers) are shown to be particular cases of the same sequence array $g(n,m)$= (2n+m)!/(m!n!(n+1)!) . Some features of the sequence array are pointed out and a unique generating function is proposed.
Classification : 11B83, 05A15, 11Y55, 11B65
Keywords: generating function, Catalan numbers, binomial identity, polynomials (Concerned with sequences A007004 
@article{JIS_2003__6_1_a3,
     author = {Cossali, G.E.},
     title = {A common generating function for {Catalan} numbers and other integer sequences},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2003__6_1_a3/}
}
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Cossali, G.E. A common generating function for Catalan numbers and other integer sequences. Journal of integer sequences, Tome 6 (2003) no. 1. http://geodesic.mathdoc.fr/item/JIS_2003__6_1_a3/