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A013318 arctanh(exp(x)-cos(x))=x+2/2!*x^2+3/3!*x^3+24/4!*x^4+165/5!*x^5... 0
0, 1, 2, 3, 24, 165, 1202, 12663, 149744, 1945065, 29307362, 489387723, 8915702664, 178036818765, 3852374482322, 89628609049983, 2235770536642784, 59498096957789265, 1681835781220294082 (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 = 0.60134676772581981740108057557172913327... is the root of the equation exp(r)-cos(r) = 1. - Vaclav Kotesovec, Feb 05 2015

MATHEMATICA

CoefficientList[Series[ArcTanh[E^x - Cos[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 05 2015 *)

CROSSREFS

Sequence in context: A047157 A003221 A013312 * A193338 A326226 A291262

Adjacent sequences:  A013315 A013316 A013317 * A013319 A013320 A013321

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

Offset changed to 0 and added a(0)=0 by Vaclav Kotesovec, Feb 05 2015

STATUS

approved

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Last modified October 14 14:39 EDT 2019. Contains 328019 sequences. (Running on oeis4.)