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
KEYWORD
sign
AUTHOR
Ralf Stephan, Dec 28 2004
STATUS
approved