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A012292

Expansion of e.g.f. arctanh(sin(x)*exp(x)) = x+2/2!*x^2+4/3!*x^3+24/4!*x^4+180/5!*x^5...

0, 1, 2, 4, 24, 180, 1432, 14544, 176064, 2382800, 36330272, 618520384, 11562021504, 235623136320, 5205288291712, 123834383495424, 3155999144761344, 85799392788650240, 2478387574846218752

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OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..414

FORMULA

a(n) ~ 1/2 * (n-1)! / r^n, where r = 0.588532743981861... is the real root of the equation sin(r) = exp(-r). - Vaclav Kotesovec, Oct 25 2013

EXAMPLE

E.g.f. = x + 2*x^2/2! + 4*x^3/3! + 24*x^4/4! + 180*x^5/5! + ...

MATHEMATICA

CoefficientList[Series[ArcTanh[Sin[x]*Exp[x]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 24 2013 *)

PROG

(PARI) x='x+O('x^30); concat([0], Vec(serlaplace(atanh(sin(x)*exp(x))))) \\ G. C. Greubel, Oct 26 2018

(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Argtanh(Sin(x)*Exp(x)) )); [0] cat [Factorial(n)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 26 2018

CROSSREFS

Sequence in context: A009672 A018988 A012587 * A211934 A012592 A121892

Adjacent sequences: A012289 A012290 A012291 * A012293 A012294 A012295

KEYWORD

nonn

AUTHOR

Patrick Demichel (patrick.demichel(AT)hp.com)

EXTENSIONS

Prepended missing a(0)=0, Vaclav Kotesovec, Oct 24 2013

STATUS

approved