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%I #16 Sep 08 2022 08:46:18
%S 0,0,0,1,13,93,569,3225,17498,92473,480626,2471344,12620821,64183465,
%T 325644870,1650517964,8364825118,42417264804,215318284778,
%U 1094490241371,5572229572248,28417811854263,145187463285629,743117432099859,3810434212170301,19573513999423879,100721431862571196
%N a(n) = floor((2*n+2)^n/(n+1)!) - binomial(2*n,n).
%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="/A282709/b282709.txt">Table of n, a(n) for n = 0..1000</a>
%t Table[Floor[(2 n + 2)^n/(n + 1)!] - Binomial[2 n, n], {n, 0, 30}] (* _Vincenzo Librandi_, Feb 27 2017 *)
%o (Magma) [Floor((2*n+2)^n/Factorial(n+1))-Binomial(2*n,n): n in [0..30]]; // _Vincenzo Librandi_, Feb 27 2017
%Y Cf. A282708, A282710.
%K nonn
%O 0,5
%A _N. J. A. Sloane_, Feb 26 2017
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