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 A213068 #16 Aug 19 2018 03:00:10
%S A213068 0,-1,5,-31,-85,4919,1248125,-158970631,2094813635,2311829506319,
%T A213068 -210731879464555,-109642894428121231,37051431528058442555,
%U A213068 4409666909576599299719,-6492299377660512249146035,648925901618982079024132169
%N A213068 Expansion of e.g.f. arcsinh(sech(x)^2), even powers only.
%C A213068 This function is even, with constant term arcsinh(1) = 0.881373587019543...
%H A213068 Vincenzo Librandi, <a href="/A213068/b213068.txt">Table of n, a(n) for n = 0..100</a>
%F A213068 E.g.f.: (arcsinh(sech(x)^2) - arcsinh(1))/sqrt(2).
%e A213068 (arcsinh(sech(x)^2) - arcsinh(1))/sqrt(2) = -x^2/2 + 5*x^4/4! - 31*x^6/6! - 85*x^8/8! + ...
%t A213068 Part[#, Range[1, Length[#], 2]] &@(Array[#! &, Length[#], 0]*#) &@ CoefficientList[Series[(ArcSinh[Sech[x]^2] - ArcSinh[1])/Sqrt[2], {x, 0, 30}], x] // ExpandAll
%Y A213068 Cf. A213066, A213067, A213069.
%K A213068 sign
%O A213068 0,3
%A A213068 _Olivier Gérard_, Jun 04 2012