Geodesic
A further generalization of the Catalan numbers and its explicit formula and integral representation
Filomat, Tome 37 (2023) no. 19, p. 6505

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DOI

In the paper, motivated by the generating function of the Catalan numbers in combinatorial number theory and with the aid of Cauchy's integral formula in complex analysis, the authors generalize the Catalan numbers and its generating function, establish an explicit formula and an integral representation for the generalization of the Catalan numbers and corresponding generating function, and derive several integral formulas and combinatorial identities.
DOI : 10.2298/FIL2319505L
Classification : 05A15, 11B75, 11B83, 26A09, 30E20, 33B15, 41A58
Keywords: Catalan number, Catalan–Qi number, Generating function, Generalization, Explicit formula, Integral representation, Cauchy’s integral formula, Integral formula, Combinatorial identity, Gamma function 
Wen-Hui Li; Omran Kouba; Issam Kaddoura; Feng Qi. A further generalization of the Catalan numbers and its explicit formula and integral representation. Filomat, Tome 37 (2023) no. 19, p. 6505 . doi: 10.2298/FIL2319505L
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     title = {A further generalization of the {Catalan} numbers and its explicit formula and integral representation},
     journal = {Filomat},
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     year = {2023},
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     doi = {10.2298/FIL2319505L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2319505L/}
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