A213068 Expansion of e.g.f. arcsinh(sech(x)^2), even powers only.

0, -1, 5, -31, -85, 4919, 1248125, -158970631, 2094813635, 2311829506319, -210731879464555, -109642894428121231, 37051431528058442555, 4409666909576599299719, -6492299377660512249146035, 648925901618982079024132169

Offset: 0

Author

Olivier Gérard, Jun 04 2012

Keywords

• sign

Comments

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

Examples

			(arcsinh(sech(x)^2) - arcsinh(1))/sqrt(2) = -x^2/2 + 5*x^4/4! - 31*x^6/6! - 85*x^8/8! + ...
		

Links

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

Crossrefs

Cf. A213066, A213067, A213069.

Programs

Mathematica

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

Formula

E.g.f.: (arcsinh(sech(x)^2) - arcsinh(1))/sqrt(2).