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Nearest integer to n!/(2*log(2)^(n+1)).
1

%I #11 Dec 28 2017 10:34:57

%S 1,1,3,13,75,541,4683,47293,545835,7087261,102247563,1622632573,

%T 28091567595,526858348381,10641342970443,230283190977853,

%U 5315654681981355,130370767029135900,3385534663256845326

%N Nearest integer to n!/(2*log(2)^(n+1)).

%C Agrees with A000670 for 0 <= n <= 16.

%D H. S. Wilf, Generatingfunctionology, Academic Press, NY, 1990, p. 147.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlmostInteger.html">Almost Integer.</a>

%H H. S. Wilf, <a href="http://www.math.upenn.edu/~wilf/DownldGF.html">Generatingfunctionology</a>, 2nd edn., Academic Press, NY, 1994, p. 176, Eq. 5.2.8.

%t Table[(1/2)*n!/Log[2]^(n+1) // Round, {n, 0, 18}] (* _Jean-François Alcover_, Dec 28 2017 *)

%Y Dominant term in an infinite series for A000670.

%K nonn

%O 0,3

%A _Dean Hickerson_, Oct 01 1998