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