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A213069
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Expansion of e.g.f. arcsinh(cos(x)*sech(x)), even powers only.
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3
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0, -1, 3, -1, -77, -13921, 791043, 23892959, -3518362637, -801110007361, 149920222346883, 24069808471917119, -7334638751184472397, -2673575321959933341601, 1059696929013386749787523, 413637485668406346391368479
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OFFSET
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0,3
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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(cos(x)*sech(x))-arcsinh(1))/sqrt(2).
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EXAMPLE
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(arcsinh(cos(x)*sech(x))-arcsinh(1))/sqrt(2) = -x^2/2 + 3*x^4/4! - x^6/6! - 77*x^8/8! + ...
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MATHEMATICA
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Part[#, Range[1, Length[#], 2]] &@(Array[#! &, Length[#], 0]*#) &@ CoefficientList[Series[(ArcSinh[Cos[x]*Sech[x]] - ArcSinh[1])/Sqrt[2], {x, 0, 30}], x] // ExpandAll
With[{nn=30}, Take[CoefficientList[Series[(ArcSinh[Cos[x]Sech[x]]-ArcSinh[ 1])/ Sqrt[2], {x, 0, nn}], x]Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Mar 24 2013 *)
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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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