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A012416
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arctanh(arctan(x)*exp(x))=x+2/2!*x^2+3/3!*x^3+20/4!*x^4+173/5!*x^5...
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0
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0, 1, 2, 3, 20, 173, 1190, 11039, 140968, 1855481, 26494858, 441706331, 8105309500, 159190672613, 3403623626286, 78823813121975, 1949180731782480, 51354602068725361, 1439864769232356882
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ (n-1)! / (2 * r^n), where r = 0.606555409757505028513842694060977136299... is the root of the equation arctan(r)*exp(r) = 1. - Vaclav Kotesovec, Feb 05 2015
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MATHEMATICA
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With[{nn=25}, CoefficientList[Series[ArcTanh[ArcTan[x]Exp[x]], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Oct 21 2011 *)
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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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EXTENSIONS
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STATUS
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approved
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