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%I #10 Feb 16 2018 16:30:14
%S 1,1,5,47,657,12219,283257,7837423,250764161,9046988147,359958186777,
%T 15446916156231,696035549765025,31596603724765195,1320452505741997625,
%U 35237128887524220383,-2148849686515840130559,-600767230517127657730077,-91881507441808204259686119
%N a(n) = (2*n)^n+(2*n+1)^n-(2*n+2)^n.
%C Theorem: (2*n)^n > (2*n+1)^n + (2*n+2)^n for 1 <= n <= 15.
%D D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, 1970; p. 192, 3.1.13.
%H Robert Israel, <a href="/A127696/b127696.txt">Table of n, a(n) for n = 0..351</a>
%F a(n) = (2*n)^n*(1+sqrt(e)-e + O(1/n)) as n -> infinity. - _Robert Israel_, Feb 16 2018
%p f:= n -> (2*n)^n+(2*n+1)^n-(2*n+2)^n:
%p map(f, [$0..30]); # _Robert Israel_, Feb 16 2018
%K sign
%O 0,3
%A _N. J. A. Sloane_, Apr 03 2007
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