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%I #13 Sep 08 2022 08:45:16
%S 1,-1,-7,-145,-6095,-433025,-46676375,-7108596625,-1454225641375,
%T -384836032842625,-127950804666254375,-52219402100109700625,
%U -25668587693366081579375,-14959038795678519196890625,-10198912212548907619042984375,-8042754039731999959020139140625
%N Expansion of e.g.f. cos(arctanh(x)), even powers only.
%H Vincenzo Librandi, <a href="/A102059/b102059.txt">Table of n, a(n) for n = 1..100</a>
%e cos(arctanh(x)) = 1 - x^2/2 - 7x^4/4! - 145x^6/6! - 6095x^8/8! - ...
%t nmax=20; Table[(CoefficientList[Series[Cos[ArcTanh[x]],{x,0,2*nmax}],x] * Range[0,2*nmax]!)[[n]],{n,1,2*nmax,2}] (* _Vaclav Kotesovec_, Nov 06 2014 *)
%o (Magma) m:=35; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1+Cos(Argtanh(x)))); [1] cat [Factorial(n-1)*b[n]: n in [3..m by 2]]; // _Vincenzo Librandi_, Aug 16 2018
%Y Bisection of A002019.
%K sign
%O 1,3
%A _Ralf Stephan_, Dec 28 2004
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