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A012416 arctanh(arctan(x)*exp(x))=x+2/2!*x^2+3/3!*x^3+20/4!*x^4+173/5!*x^5... 0
0, 1, 2, 3, 20, 173, 1190, 11039, 140968, 1855481, 26494858, 441706331, 8105309500, 159190672613, 3403623626286, 78823813121975, 1949180731782480, 51354602068725361, 1439864769232356882 (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 = 0.606555409757505028513842694060977136299... is the root of the equation arctan(r)*exp(r) = 1. - Vaclav Kotesovec, Feb 05 2015

MATHEMATICA

With[{nn=25}, CoefficientList[Series[ArcTanh[ArcTan[x]Exp[x]], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Oct 21 2011 *)

CROSSREFS

Sequence in context: A009721 A013340 A218873 * A261317 A177946 A006246

Adjacent sequences:  A012413 A012414 A012415 * A012417 A012418 A012419

KEYWORD

nonn,changed

AUTHOR

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

EXTENSIONS

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

STATUS

approved

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Last modified December 8 19:05 EST 2016. Contains 278948 sequences.