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

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Cf. A000828, A000831.

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

Programs

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 *)

Formula

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