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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 (list; graph; refs; listen; history; text; internal format)
 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:=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 Adjacent sequences: A012298 A012299 A012300 * A012302 A012303 A012304 KEYWORD sign AUTHOR Patrick Demichel (patrick.demichel(AT)hp.com) EXTENSIONS a(0)=0 prepended by Vaclav Kotesovec, Feb 08 2015 STATUS approved

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Last modified February 21 07:54 EST 2024. Contains 370219 sequences. (Running on oeis4.)