login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A012416 arctanh(arctan(x)*exp(x))=x+2/2!*x^2+3/3!*x^3+20/4!*x^4+173/5!*x^5... 0

%I #12 Nov 28 2016 18:32:17

%S 0,1,2,3,20,173,1190,11039,140968,1855481,26494858,441706331,

%T 8105309500,159190672613,3403623626286,78823813121975,

%U 1949180731782480,51354602068725361,1439864769232356882

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

%F 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

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

%K nonn

%O 0,3

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

%E Prepended missing a(0)=0 from _Vaclav Kotesovec_, Feb 05 2015

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 01:22 EDT 2024. Contains 370952 sequences. (Running on oeis4.)