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A012830
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arctanh(sec(x)*arcsinh(x))=x+4/3!*x^3+88/5!*x^5+4184/7!*x^7...
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0
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1, 4, 88, 4184, 398848, 58835456, 12993783424, 3911934210560, 1562951627091968, 793328025614454784, 501079933291827593216, 384338283691725654392832, 352458553186266111883247616
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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 = 0.7759352114645266952650140305350722729253... is the root of the equation sec(r)*arcsinh(r) = 1. - Vaclav Kotesovec, Feb 05 2015
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MATHEMATICA
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nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcSinh[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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