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Floor( 2*(2*n+1)^n*sinh(1/2) ) - (2*n+2)^n + (2*n)^n.
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%I #9 Feb 15 2014 12:32:03

%S 1,1,6,61,933,19013,486903,15046084,545075629,22661379274,

%T 1063692556445,55646541997466,3210791930531340,202576381691155974,

%U 13874616146693093852,1025250869305088941530,81303554487412360191076,6887348857934410851161581,620720182437520911247158798

%N Floor( 2*(2*n+1)^n*sinh(1/2) ) - (2*n+2)^n + (2*n)^n.

%C Theorem: 2*(2*n+1)^n*sinh(1/2) > (2*n+2)^n - (2*n)^n for n >= 1.

%D D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, 1970; p. 192, 3.1.13.

%t Join[{1},Table[Floor[2(2n+1)^n Sinh[1/2]]-(2n+2)^n+(2n)^n,{n,20}]] (* _Harvey P. Dale_, Jun 20 2011 *)

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Apr 03 2007