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%I #14 Apr 10 2024 08:47:02
%S 0,1,7,61,617,7761,117601,2097047,43046337,999999055,25937420761,
%T 743008360293,23298085076401,793714773119009,29192926024745505,
%U 1152921504604819951,48661191875656546561,2185911559738662072543,104127350297911055738281,5242879999999999345270925
%N a(n) = (n+1)^n - n!!.
%C Theorem: (n+1)^n > n!! for n>0.
%D D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, 1970; p. 192, 3.1.15.
%H Michael De Vlieger, <a href="/A127688/b127688.txt">Table of n, a(n) for n = 0..386</a>
%p seq((n+1)^n - doublefactorial(n), n=0..10); # _Georg Fischer_, Apr 10 2024
%t Table[(n+1)^n - (n)!!, {n, 0, 10}] (* _Georg Fischer_, Apr 10 2024 *)
%Y Cf. A000165, A127650.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Apr 03 2007
%E Formula changed by _Georg Fischer_, Apr 10 2024