Geodesic
Asymptotic expansions of central binomial coefficients and Catalan numbers
Journal of integer sequences, Tome 17 (2014) no. 2.

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

Summary: We give a systematic view of the asymptotic expansion of two well-known sequences, the central binomial coefficients and the Catalan numbers. The main point is explanation of the nature of the best shift in variable $n$, in order to obtain "nice" asymptotic expansions. We also give a complete asymptotic expansion of partial sums of these sequences.
Classification : 11B65, 41A60, 33B15
Keywords: binomial coefficient, Catalan number, asymptotic expansion, gamma function 
@article{JIS_2014__17_2_a2,
     author = {Elezovi\'c, Neven},
     title = {Asymptotic expansions of central binomial coefficients and {Catalan} numbers},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_2_a2/}
}
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Elezović, Neven. Asymptotic expansions of central binomial coefficients and Catalan numbers. Journal of integer sequences, Tome 17 (2014) no. 2. http://geodesic.mathdoc.fr/item/JIS_2014__17_2_a2/