Journal of Integer Sequences, Vol. 17 (2014), Article 14.2.1

Asymptotic Expansions of Central Binomial Coefficients and Catalan Numbers

Neven Elezović
Faculty of Electrical Engineering and Computing
University of Zagreb
Unska 3
10000 Zagreb


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.

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(Concerned with sequences A001163 A001164 A046968 A046969.)

Received March 21 2013; revised versions received June 6 2013; October 14 2013; November 26 2013. Published in Journal of Integer Sequences, January 3 2014.

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