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%I #13 Sep 08 2022 08:46:18
%S 0,0,0,4,18,81,338,1384,5588,22405,89430,355906,1413600,5607109,
%T 22220902,88008656,348435254,1379169043,5458320734,21601368452,
%U 85488832259,338346669389,1339221309614,5301399720197,20988604614673,83106763866881,329118546749196,1303568050309469,5163945978762924
%N a(n) = binomial(2*n,n) - ceiling(2^(2*n)/(n+1)).
%C a(n) >= 0.
%D P. S. Bullen, A Dictionary of Inequalities, Longman, 1998. See p. 34.
%D D. S. Mitrinovic, Analytic Inequalities, Springer 1970. See (3.1.28).
%H Vincenzo Librandi, <a href="/A282708/b282708.txt">Table of n, a(n) for n = 0..1000</a>
%t Table[Binomial[2 n, n] - Ceiling[2^(2 n)/(n + 1)], {n, 0, 40}] (* _Vincenzo Librandi_, Feb 27 2017 *)
%o (Magma) [Binomial(2*n,n)-Ceiling(2^(2*n)/(n+1)): n in [0..30]]; // _Vincenzo Librandi_, Feb 27 2017
%Y Cf. A282709, A282710.
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Feb 26 2017