This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A213067 #15 Feb 24 2022 16:52:38
%S A213067 0,-1,-2,44,1408,-18016,-5095232,-139605376,56961507328,8306292414464,
%T A213067 -1178066937638912,-640316054325354496,-7088737339266301952,
%U A213067 76268423227563817631744,18895160315230467816030208,-12297988177132848140606242816
%N A213067 E.g.f.: arctan(cos(x)^2) - Pi/4.
%C A213067 This function is even, with constant term Pi/4 = 0.785398163397...
%C A213067 It was missing from OEIS entries by Patrick Demichel.
%H A213067 Vincenzo Librandi, <a href="/A213067/b213067.txt">Table of n, a(n) for n = 0..100</a>
%F A213067 E.g.f.: arctan(cos(x)^2) - Pi/4.
%e A213067 arctan(cos(x)^2) - Pi/4 = 0 - x^2/2 - 2*x^4/4! + 44*x^6/6! + 1408*x^8/8! + ...
%t A213067 Part[#, Range[1, Length[#], 2]] &@(Array[#! &, Length[#], 0]*#) &@
%t A213067 CoefficientList[Series[ArcTan[Cos[x]^2] - Pi/4, {x, 0, 30}], x] // ExpandAll
%t A213067 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 *)
%Y A213067 Cf. A213066, A213068, A213069.
%K A213067 sign
%O A213067 0,3
%A A213067 _Olivier Gérard_, Jun 04 2012