login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A213067 E.g.f.: arctan(cos(x)^2) - Pi/4. 3
0, -1, -2, 44, 1408, -18016, -5095232, -139605376, 56961507328, 8306292414464, -1178066937638912, -640316054325354496, -7088737339266301952, 76268423227563817631744, 18895160315230467816030208, -12297988177132848140606242816 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

It was missing from OEIS entries by Patrick Demichel.

LINKS

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

FORMULA

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A213066, A213068, A213069.

Sequence in context: A001627 A202747 A094397 * A140795 A161744 A208045

Adjacent sequences:  A213064 A213065 A213066 * A213068 A213069 A213070

KEYWORD

sign

AUTHOR

Olivier Gérard, Jun 04 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 15 18:38 EDT 2022. Contains 356148 sequences. (Running on oeis4.)