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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<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 A285850

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 July 5 17:29 EDT 2020. Contains 335473 sequences. (Running on oeis4.)