OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..220
FORMULA
a(n) ~ (-1)^(n+1) * (2*n-1)! / (log(1+sqrt(2)))^(2*n). - Vaclav Kotesovec, Feb 08 2015
EXAMPLE
E.g.f. = 2*x^2/2! - 8*x^4/4! + 272*x^6/6! - 13568*x^8/8! + ...
MAPLE
seq(coeff(series(factorial(n)*arctanh(sin(x)*sin(x)), x, n+1), x, n), n = 0 .. 26, 2); # Muniru A Asiru, Oct 26 2018
MATHEMATICA
nn = 20; Table[(CoefficientList[Series[ArcTanh[Sin[x]^2], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 08 2015 *)
PROG
(PARI) x='x+O('x^50); v=Vec(serlaplace(atanh(sin(x)*sin(x)))); concat([0], vector(#v\2, n, v[2*n-1])) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Argtanh(Sin(x)^2) )); [0] cat [Factorial(2*n+2)*b[2*n+1]: n in [0..Floor((m-4)/2)]]; // G. C. Greubel, Oct 25 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
EXTENSIONS
a(0)=0 prepended by Vaclav Kotesovec, Feb 08 2015
STATUS
approved