OFFSET
0,3
COMMENTS
This function is even, with constant term arcsinh(1) = 0.881373587019543...
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..100
FORMULA
E.g.f.: (arcsinh(cos(x)*sech(x))-arcsinh(1))/sqrt(2).
EXAMPLE
(arcsinh(cos(x)*sech(x))-arcsinh(1))/sqrt(2) = -x^2/2 + 3*x^4/4! - x^6/6! - 77*x^8/8! + ...
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Olivier Gérard, Jun 04 2012
STATUS
approved