Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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