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%I #19 Sep 08 2022 08:45:56
%S 1,2,4,9,26,77,246,805,2702,9238,32066,112674,400024,1432736,5170584,
%T 18783763,68635478,252087092,930138522,3446163221,12815663678,
%U 47820430994,178987624514,671825076732,2528212128756,9536894864387,36054433808299,136583760727865,518401146543812,1971076359414358,7506908923471954,28634752202227978
%N a(n) = ceiling(binomial(2*n-1,n-1)/n).
%C A useful lower bound when studying certain problems involving compositions.
%H Vincenzo Librandi, <a href="/A188669/b188669.txt">Table of n, a(n) for n = 1..1000</a>
%t Table[Ceiling[Binomial[2 n - 1, n - 1]/n], {n, 35}] (* _Harvey P. Dale_, Apr. 09 2011 *)
%o (Magma) [Ceiling(Binomial(2*n-1,n-1)/n): n in [1..60]]; // _Vincenzo Librandi_, Sep 07 2016
%Y See A201058, A201059 for numerators and denominators without ceiling. - _F. Chapoton_, Aug 15 2021
%K nonn
%O 1,2
%A Robert Gerbicz and _N. J. A. Sloane_, Apr 07 2011