A296467 Expansion of e.g.f. arctan(arctanh(x)) (odd powers only).

1, 0, 8, 112, 8192, 599808, 80010240, 13537247232, 3160676007936, 929451393220608, 343173318976733184, 154043745649772986368, 82935056810462020632576, 52660879605487383997317120, 38970318170642827020431523840, 33236188662933234332228627988480, 32365907321554306913981616441262080

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