A012200 - OEIS

A012200

arctanh(arctan(arcsin(x))) = x + 1/3!*x^3 + 17/5!*x^5 + 393/7!*x^7 + 25601/9!*x^9 + ...

1, 1, 17, 393, 25601, 2044241, 289407505, 49702166681, 12331304386689, 3665631364571297, 1415269826057944465, 644290354204397460137, 358377106160586506065793, 231185244070754402809628657

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OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..220

FORMULA

Conjecture: a(n) ~ (2*n)! / (sin(tan(1)))^(2*n+1). Because sin(tan(1)) = 0.9999103740052..., is not possible to verify this numerically from 1000 terms. - Vaclav Kotesovec, Feb 07 2015

MATHEMATICA

nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcTan[ArcSin[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: A012639 A350926 A327732 * A340972 A340353 A007925

Adjacent sequences: A012197 A012198 A012199 * A012201 A012202 A012203

KEYWORD

nonn

AUTHOR

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

STATUS

approved