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A013005
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arctanh(arctan(x)+tan(x))=2*x+16/3!*x^3+808/5!*x^5+98432/7!*x^7...
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0
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2, 16, 808, 98432, 22498432, 8253398272, 4441967893504, 3295980115392512, 3225082749950656512, 4023514822062532460544, 6233513843421340514123776, 11741363464465799639674126336
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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 = 0.4952542103931914966377065988697787139312... is the root of the equation arctan(r)+tan(r) = 1. - Vaclav Kotesovec, Feb 05 2015
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MATHEMATICA
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nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcTan[x] + Tan[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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