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

1,3

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Bisection of A002019.

Sequence in context: A296684 A012826 A232363 * A064624 A342113 A211108

Adjacent sequences: A102056 A102057 A102058 * A102060 A102061 A102062

Keyword

sign

Author

Ralf Stephan, Dec 28 2004

Status

approved