Geodesic
Asymptotic expansions of central binomial coefficients and Catalan numbers
Journal of integer sequences, Tome 17 (2014) no. 2
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},
     year = {2014},
     volume = {17},
     number = {2},
     zbl = {1317.11023},
     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/