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%I #16 Feb 02 2018 02:51:44
%S 0,1,1,-29,211,20161,-1206479,-54804749,16984806931,-363209849759,
%T -519143744434559,87734755669460131,25846367065418224051,
%U -14672317296701543650079,-716886263478049393332239,3283895381829696830969594611
%N E.g.f.: (arcsinh(cosh(x)^2) - arcsinh(1))/sqrt(2), (even terms only).
%C This function is even, with constant term arcsinh(1) = 0.881373587019543...
%H Vincenzo Librandi, <a href="/A213066/b213066.txt">Table of n, a(n) for n = 0..100</a>
%F E.g.f.: (arcsinh(cosh(x)^2)-arcsinh(1))/sqrt(2), even terms only.
%e (arcsinh(cosh(x)^2)-arcsinh(1))/sqrt(2) = 0 + x^2/2 + x^4/4! - 29*x^6/6! + 211*x^8/8! + ...
%t Part[#, Range[1, Length[#], 2]] &@(Array[#! &, Length[#], 0]*#) &@ CoefficientList[Series[(ArcSinh[Cosh[x]^2] - ArcSinh[1])/Sqrt[2], {x, 0, 30}], x] // ExpandAll
%o (PARI) x='x+O('x^30); v=Vec(serlaplace((asinh(cosh(x)^2) - asinh(1) )/sqrt(2))); round(vector(#v\2,n,v[2*n-1])) \\ _G. C. Greubel_, Feb 01 2018
%K sign
%O 0,4
%A _Olivier Gérard_, Jun 04 2012
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