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A012920
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arctanh(arcsin(x)+sin(x))=2*x+16/3!*x^3+778/5!*x^5+94064/7!*x^7...
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0
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2, 16, 778, 94064, 21203218, 7679356144, 4079013377242, 2987290363267664, 2884950332801855778, 3552295906912003762512, 5431778247093958269249706, 10097951729467246217104155568
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OFFSET
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0,1
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Patrick Demichel (patrick.demichel(AT)hp.com)
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STATUS
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approved
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