A102059 Expansion of e.g.f. cos(arctanh(x)), even powers only.

1, -1, -7, -145, -6095, -433025, -46676375, -7108596625, -1454225641375, -384836032842625, -127950804666254375, -52219402100109700625, -25668587693366081579375, -14959038795678519196890625, -10198912212548907619042984375, -8042754039731999959020139140625

Offset: 1

Author

Ralf Stephan, Dec 28 2004

Keywords

• sign

Examples

			cos(arctanh(x)) = 1 - x^2/2 - 7x^4/4! - 145x^6/6! - 6095x^8/8! - ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..100

Crossrefs

Bisection of A002019.

Programs

Magma

m:=35; R:=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

Mathematica

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 *)