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A275711 Nearest integer to 2*n!*(2/Pi)^(n+1). 1

%I

%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

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Last modified March 18 12:10 EDT 2019. Contains 321283 sequences. (Running on oeis4.)