A102058 Expansion of e.g.f. sin(arctanh(x)), odd powers only.

1, 1, 5, 5, -5815, -956375, -172917875, -38579649875, -10713341611375, -3663118565923375, -1519935859717136875, -754429769289426936875, -442113820341129750734375, -302333022017412857174234375, -238762676857713027642764171875, -215766282905942334008224968671875

Offset: 1

Author

Ralf Stephan, Dec 28 2004

Keywords

• sign

Examples

			sin(arctanh(x)) = x + x^3/3! + 5x^5/5! + 5x^7/7! - 5815x^9/9! - ...
		

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+Sin(Argtanh(x)))); [Factorial(n-1)*b[n]: n in [2..m by 2]]; // Vincenzo Librandi, Aug 16 2018

Mathematica

nmax=20; Table[(CoefficientList[Series[Sin[ArcTanh[x]],{x,0,2*nmax}],x] * Range[0,2*nmax-1]!)[[n]],{n,2,2*nmax,2}] (* Vaclav Kotesovec, Nov 06 2014 *)

Maxima

a(n):=(2*n-1)!*sum((-1)^(i)*sum((stirling1(k+2*i+1,2*i+1)*2^(k)* binomial(2*n-2,k+2*i))/(k+2*i+1)!,k,0,2*n-1-2*i-1),i,0,n-1); /* Vladimir Kruchinin, Dec 12 2011 */

Formula

a(n) = (2*n-1)!*Sum(i=0..n-1, (-1)^(i)*Sum(k=0..2*n-1-2*i-1, (stirling1(k+2*i+1,2*i+1)*2^(k)* binomial(2*n-2,k+2*i))/(k+2*i+1)!)). - Vladimir Kruchinin, Dec 12 2011