OFFSET
0,4
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(cosh(x)^2)-arcsinh(1))/sqrt(2), even terms only.
EXAMPLE
(arcsinh(cosh(x)^2)-arcsinh(1))/sqrt(2) = 0 + x^2/2 + x^4/4! - 29*x^6/6! + 211*x^8/8! + ...
MATHEMATICA
Part[#, Range[1, Length[#], 2]] &@(Array[#! &, Length[#], 0]*#) &@ CoefficientList[Series[(ArcSinh[Cosh[x]^2] - ArcSinh[1])/Sqrt[2], {x, 0, 30}], x] // ExpandAll
PROG
(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
CROSSREFS
KEYWORD
sign
AUTHOR
Olivier Gérard, Jun 04 2012
STATUS
approved