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A213066
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E.g.f.: (arcsinh(cosh(x)^2) - arcsinh(1))/sqrt(2), (even terms only).
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4
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0, 1, 1, -29, 211, 20161, -1206479, -54804749, 16984806931, -363209849759, -519143744434559, 87734755669460131, 25846367065418224051, -14672317296701543650079, -716886263478049393332239, 3283895381829696830969594611
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OFFSET
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0,4
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COMMENTS
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This function is even, with constant term arcsinh(1) = 0.881373587019543...
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LINKS
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FORMULA
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E.g.f.: (arcsinh(cosh(x)^2)-arcsinh(1))/sqrt(2), even terms only.
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EXAMPLE
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(arcsinh(cosh(x)^2)-arcsinh(1))/sqrt(2) = 0 + x^2/2 + x^4/4! - 29*x^6/6! + 211*x^8/8! + ...
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MATHEMATICA
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Part[#, Range[1, Length[#], 2]] &@(Array[#! &, Length[#], 0]*#) &@ CoefficientList[Series[(ArcSinh[Cosh[x]^2] - ArcSinh[1])/Sqrt[2], {x, 0, 30}], x] // ExpandAll
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PROG
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(PARI) x='x+O('x^30); v=Vec(serlaplace((asinh(cosh(x)^2) - asinh(1) )/sqrt(2))); round(vector(#v\2, n, v[2*n-1])) \\ G. C. Greubel, Feb 01 2018
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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