%I #16 Mar 23 2018 17:35:27
%S 1,1,1,2,5,16,61,272,1385,7936,50521,353791,2702767,22368251,
%T 199360995,1903757268,19391512295,209865342434,2404879677510,
%U 29088885104489,370371188272931,4951498052966308,69348874393874527,1015423886503257017,15514534163575397655
%N Nearest integer to 2*n!*(2/Pi)^(n+1).
%C For n odd, approximation to the tangent (or "Zag") numbers A000182. For n even, approximation to the secant (or "Zig") numbers A000364. The first difference from the Euler (or "up/down") numbers A000111 occurs for a(11)=353791 /= A000111(11)=353792.
%H Hugo Pfoertner, <a href="/A275711/b275711.txt">Table of n, a(n) for n = 0..100</a>
%H P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/book.pdf">Analytic Combinatorics</a>, Cambridge University Press, 2009, pages 2-5.
%F a(n) = round (2*n!*(2/Pi)^(n+1)).
%t Table[Round[2*n!*(2/Pi)^(n+1)],{n,0,30}] (* _Harvey P. Dale_, Jun 18 2017 *)
%Y Cf. A000111, A000182, A000364.
%K nonn
%O 0,4
%A _Hugo Pfoertner_, Aug 06 2016