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A012810
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arctanh(sec(x)*arctan(x))=x+3/3!*x^3+73/5!*x^5+2779/7!*x^7...
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0
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1, 3, 73, 2779, 260177, 32853491, 6787498521, 1803655970635, 660549566885793, 299826162055728355, 172107541834064358121, 118707937911469881769147, 98574741929922225569568241
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ (2*n)! / r^(2*n+1), where r = 0.81654122617273381556779185061232051824097... is the root of the equation sec(r)*arctan(r) = 1. - Vaclav Kotesovec, Feb 05 2015
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MATHEMATICA
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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 *)
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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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