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A012810 arctanh(sec(x)*arctan(x))=x+3/3!*x^3+73/5!*x^5+2779/7!*x^7... 0
1, 3, 73, 2779, 260177, 32853491, 6787498521, 1803655970635, 660549566885793, 299826162055728355, 172107541834064358121, 118707937911469881769147, 98574741929922225569568241 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) ~ (2*n)! / r^(2*n+1), where r = 0.81654122617273381556779185061232051824097... is the root of the equation sec(r)*arctan(r) = 1. - Vaclav Kotesovec, Feb 05 2015

MATHEMATICA

nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcTan[x]*Sec[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 05 2015 *)

CROSSREFS

Sequence in context: A173807 A093165 A189306 * A020517 A119017 A307232

Adjacent sequences:  A012807 A012808 A012809 * A012811 A012812 A012813

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified June 14 00:02 EDT 2021. Contains 345016 sequences. (Running on oeis4.)