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URL: https://oeis.org/A012301

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A012301
Expansion of e.g.f. arctanh(sin(x)*sin(x)), even powers only.
1
0, 2, -8, 272, -13568, 1290752, -181296128, 36501112832, -9859508338688, 3453141256896512, -1520147333209653248, 821912974600193441792, -535368543762962928631808, 413509146873290771683868672
OFFSET
0,2
LINKS
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
Sequence in context: A258161 A012296 A009675 * A296406 A215651 A363180
KEYWORD
sign
EXTENSIONS
a(0)=0 prepended by Vaclav Kotesovec, Feb 08 2015
STATUS
approved