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A012726
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arctanh(arctanh(x)*tan(x))=2/2!*x^2+16/4!*x^4+560/6!*x^6+39296/8!*x^8...
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0
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0, 2, 16, 560, 39296, 4768768, 881315840, 230827284480, 81324940394496, 37097190468747264, 21272100905987080192, 14977571327515946909696, 12703902924309766749552640, 12776509288228175937154318336
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..13.
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FORMULA
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a(n) ~ (2*n-1)! / r^(2*n), where r = 0.772419882704426062944736631601064953563... is the root of the equation arctanh(r)*tan(r) = 1. - Vaclav Kotesovec, Feb 05 2015
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MATHEMATICA
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With[{nn=30}, Flatten[{0, Take[CoefficientList[Series[ArcTanh[ArcTanh[x]Tan[x]], {x, 0, nn}], x] Range[0, nn]!, {3, -1, 2}]}]] (* Harvey P. Dale, Aug 26 2014 *)
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CROSSREFS
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Sequence in context: A013136 A013004 A012679 * A013177 A060279 A012757
Adjacent sequences: A012723 A012724 A012725 * A012727 A012728 A012729
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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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Definition clarified by Harvey P. Dale, Aug 26 2014
Prepended missing a(0)=0 from Vaclav Kotesovec, Feb 05 2015
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STATUS
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approved
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