A213067 E.g.f.: arctan(cos(x)^2) - Pi/4.

0, -1, -2, 44, 1408, -18016, -5095232, -139605376, 56961507328, 8306292414464, -1178066937638912, -640316054325354496, -7088737339266301952, 76268423227563817631744, 18895160315230467816030208, -12297988177132848140606242816

Offset: 0

Author

Olivier Gérard, Jun 04 2012

Keywords

• sign

Comments

This function is even, with constant term Pi/4 = 0.785398163397...

It was missing from OEIS entries by Patrick Demichel.

Examples

			arctan(cos(x)^2) - Pi/4 = 0 - x^2/2 - 2*x^4/4! + 44*x^6/6! + 1408*x^8/8! + ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A213066, A213068, A213069.

Programs

Mathematica

Part[#, Range[1, Length[#], 2]] &@(Array[#! &, Length[#], 0]*#) &@
  CoefficientList[Series[ArcTan[Cos[x]^2] - Pi/4, {x, 0, 30}], x] // ExpandAll
With[{nn=30},Take[CoefficientList[Series[ArcTan[Cos[x]^2]-Pi/4,{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Feb 24 2022 *)

Formula

E.g.f.: arctan(cos(x)^2) - Pi/4.