A012416 arctanh(arctan(x)*exp(x))=x+2/2!*x^2+3/3!*x^3+20/4!*x^4+173/5!*x^5...

0, 1, 2, 3, 20, 173, 1190, 11039, 140968, 1855481, 26494858, 441706331, 8105309500, 159190672613, 3403623626286, 78823813121975, 1949180731782480, 51354602068725361, 1439864769232356882

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 A353921 A361028

Adjacent sequences: A012413 A012414 A012415 * A012417 A012418 A012419

Keyword

nonn

Author

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

Extensions

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

Status

approved