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A012042
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arctanh(sin(arcsinh(x)))=x+4/5!*x^5-80/7!*x^7+4240/9!*x^9-342400/11!*x^11...
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1
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1, 0, 4, -80, 4240, -342400, 41806400, -7093216000, 1601470624000, -464003651072000, 167847611351680000, -74143433704737280000, 39275771932443138560000, -24575763662119940608000000
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internal format)
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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) ~ c * (-1)^n * (2*n)! / sqrt(n), where c = sech(Pi/2)/sqrt(Pi) = 0.22485031987421343130846684736559... . - Vaclav Kotesovec, Feb 03 2015, updated Mar 17 2024
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MATHEMATICA
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nn = 20; Table[(CoefficientList[Series[ArcTanh[Sin[ArcSinh[x]]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 03 2015 *)
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CROSSREFS
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KEYWORD
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sign
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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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