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

1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936, 50521, 353791, 2702767, 22368251, 199360995, 1903757268, 19391512295, 209865342434, 2404879677510, 29088885104489, 370371188272931, 4951498052966308, 69348874393874527, 1015423886503257017, 15514534163575397655

Offset

0,4

Comments

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.

Links

Hugo Pfoertner, Table of n, a(n) for n = 0..100

P. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge University Press, 2009, pages 2-5.

Formula

a(n) = round (2*n!*(2/Pi)^(n+1)).

Mathematica

Table[Round[2*n!*(2/Pi)^(n+1)], {n, 0, 30}] (* Harvey P. Dale, Jun 18 2017 *)

Crossrefs

Cf. A000111, A000182, A000364.

Sequence in context: A322616 A178123 A138265 * A163747 A346838 A000111

Adjacent sequences: A275708 A275709 A275710 * A275712 A275713 A275714

Keyword

nonn

Author

Hugo Pfoertner, Aug 06 2016

Status

approved