A013340 - OEIS

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A013340

arctanh(exp(x)-sech(x))=x+2/2!*x^2+3/3!*x^3+20/4!*x^4+165/5!*x^5...

0, 1, 2, 3, 20, 165, 1142, 10983, 136040, 1753545, 25376042, 422373963, 7641560060, 149590274925, 3195495898142, 73536613981743, 1808159717424080, 47465557573756305, 1324783497842287442

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..18.

FORMULA

a(n) ~ (n-1)! / (2 * r^n), where r = log((1 + (19 - 3*sqrt(33))^(1/3) + (19 + 3*sqrt(33))^(1/3))/3) = 0.60937786343600623153680337116839869542853927931... is the root of the equation exp(r)-sech(r) = 1. - Vaclav Kotesovec, Feb 05 2015

MATHEMATICA

CoefficientList[Series[ArcTanh[Sinh[x]*(1 + Tanh[x])], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 05 2015 *)

CROSSREFS

Sequence in context: A069323 A356884 A009721 * A218873 A012416 A261317

Adjacent sequences: A013337 A013338 A013339 * A013341 A013342 A013343

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

Prepended missing a(0)=0 from Vaclav Kotesovec, Feb 05 2015

STATUS

approved