A012920 - OEIS

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A012920

arctanh(arcsin(x)+sin(x))=2*x+16/3!*x^3+778/5!*x^5+94064/7!*x^7...

2, 16, 778, 94064, 21203218, 7679356144, 4079013377242, 2987290363267664, 2884950332801855778, 3552295906912003762512, 5431778247093958269249706, 10097951729467246217104155568

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..11.

FORMULA

a(n) ~ (2*n)! / r^(2*n+1), where r = 0.4985117060766136685059797926558609110334... is the root of the equation arcsin(r)+sin(r) = 1. - Vaclav Kotesovec, Feb 05 2015

MATHEMATICA

nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcSin[x] + Sin[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: A186002 A013029 A012915 * A013088 A013137 A013990

Adjacent sequences: A012917 A012918 A012919 * A012921 A012922 A012923

KEYWORD

nonn

AUTHOR

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

STATUS

approved