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A013177 tan(arctanh(x)+arctan(x))=2*x+16/3!*x^3+560/5!*x^5+42880/7!*x^7... 0
2, 16, 560, 42880, 5692160, 1158860800, 335091660800, 130514735104000, 65860132462592000, 41792278392537088000, 32569972497977507840000, 30580999289444580720640000, 34048056335378925092864000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..12.

FORMULA

a(n) ~ (1-r^4) * (2*n+1)! / r^(2*n+2), where r = 0.734095513758912755828782788976924944882810535913453055562... is the root of the equation arctanh(r) + arctan(r) = Pi/2. Also root of equation Pi + log((1-r)/(1+r)) = arctan(2*r/(1-r^2)). - Vaclav Kotesovec, Feb 07 2015

MATHEMATICA

nn = 20; Table[(CoefficientList[Series[Tan[ArcTan[x] + ArcTanh[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 07 2015 *)

CROSSREFS

Sequence in context: A013004 A012679 A012726 * A060279 A012757 A012464

Adjacent sequences:  A013174 A013175 A013176 * A013178 A013179 A013180

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified January 19 06:18 EST 2022. Contains 350464 sequences. (Running on oeis4.)