login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A296467 Expansion of e.g.f. arctan(arctanh(x)) (odd powers only). 6
1, 0, 8, 112, 8192, 599808, 80010240, 13537247232, 3160676007936, 929451393220608, 343173318976733184, 154043745649772986368, 82935056810462020632576, 52660879605487383997317120, 38970318170642827020431523840, 33236188662933234332228627988480, 32365907321554306913981616441262080 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Robert Israel, Table of n, a(n) for n = 0..224

FORMULA

E.g.f.: arctanh(arctan(x)) (odd powers only, absolute values).

E.g.f.: i*(log(2 + i*log(1 - x) - i*log(1 + x)) - log(2 - i*log(1 - x) + i*log(1 + x)))/2, where i is the imaginary unit (odd powers only).

EXAMPLE

arctan(arctanh(x)) =  x/1! + 8*x^5/5! + 112*x^7/7! + 8192*x^9/9! + 599808*x^11/11! + 80010240*x^13/13! + ...

MAPLE

S:= series(arctan(arctanh(x)), x, 52):

seq(coeff(S, x, 2*i+1)*(2*i+1)!, i=0..25); # Robert Israel, Dec 13 2017

MATHEMATICA

nmax = 17; Table[(CoefficientList[Series[ArcTan[ArcTanh[x]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]

nmax = 17; Table[(CoefficientList[Series[I (Log[2 + I Log[1 - x] - I Log[1 + x]] - Log[2 - I Log[1 - x] + I Log[1 + x]])/2, {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]

CROSSREFS

Cf. A003721, A010050, A012231, A296465.

Sequence in context: A034689 A010041 A099703 * A164774 A259590 A155460

Adjacent sequences:  A296464 A296465 A296466 * A296468 A296469 A296470

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 13 2017

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 24 10:57 EDT 2020. Contains 337317 sequences. (Running on oeis4.)