A000825 Expansion of cos x (1 + sin x ) /cos 2x.

1, 1, 3, 8, 57, 256, 2763, 17408, 250737, 2031616, 36581523, 362283008, 7828053417, 91620376576, 2309644635483, 31191159799808, 898621108880097, 13753735117275136, 445777636063460643, 7625476699018231808

Offset

0,3

Links

R. J. Mathar, Table of n, a(n) for n = 0..200

Formula

a(n) ~ n! * (sqrt(2) + 1 + (sqrt(2)-1)*(-1)^n) * 4^n / Pi^(n+1). - Vaclav Kotesovec, Jun 01 2015

Mathematica

With[{nn=20}, CoefficientList[Series[Cos[x] (1+Sin[x])/Cos[2x], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 08 2013 *)

Crossrefs

Cf. A000828, A000831.

Bisections are A000281 and (1/2) * A012393.

Sequence in context: A308572 A101361 A104034 * A273433 A132517 A027262

Adjacent sequences: A000822 A000823 A000824 * A000826 A000827 A000828

Keyword

nonn

Author

N. J. A. Sloane

Status

approved