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

1,3

Links

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

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

Example

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

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 *)

Prog

(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 */
(Magma) m:=35; R<x>:=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

Crossrefs

Bisection of A002019.

Sequence in context: A051716 A226260 A102060 * A231409 A031364 A078473

Adjacent sequences: A102055 A102056 A102057 * A102059 A102060 A102061

Keyword

sign

Author

Ralf Stephan, Dec 28 2004

Status

approved