A213066 E.g.f.: (arcsinh(cosh(x)^2) - arcsinh(1))/sqrt(2), (even terms only).

0, 1, 1, -29, 211, 20161, -1206479, -54804749, 16984806931, -363209849759, -519143744434559, 87734755669460131, 25846367065418224051, -14672317296701543650079, -716886263478049393332239, 3283895381829696830969594611

Offset: 0

Author

Olivier Gérard, Jun 04 2012

Keywords

• sign

Comments

This function is even, with constant term arcsinh(1) = 0.881373587019543...

Examples

			(arcsinh(cosh(x)^2)-arcsinh(1))/sqrt(2) = 0 + x^2/2 + x^4/4! - 29*x^6/6! + 211*x^8/8! + ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Programs

Mathematica

Part[#, Range[1, Length[#], 2]] &@(Array[#! &, Length[#], 0]*#) &@ CoefficientList[Series[(ArcSinh[Cosh[x]^2] - ArcSinh[1])/Sqrt[2], {x, 0, 30}], x] // ExpandAll

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

Formula

E.g.f.: (arcsinh(cosh(x)^2)-arcsinh(1))/sqrt(2), even terms only.