A213067 -id:A213067 - cp's OEIS frontend

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

Olivier Gérard, Jun 04 2012

sign

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

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

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

Cf. A213066, A213067, A213069.

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

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

A213069 Expansion of e.g.f. arcsinh(cos(x)*sech(x)), even powers only.

Original entry on oeis.org

0, -1, 3, -1, -77, -13921, 791043, 23892959, -3518362637, -801110007361, 149920222346883, 24069808471917119, -7334638751184472397, -2673575321959933341601, 1059696929013386749787523, 413637485668406346391368479

Offset: 0

Olivier Gérard, Jun 04 2012

sign

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

			(arcsinh(cos(x)*sech(x))-arcsinh(1))/sqrt(2) = -x^2/2 + 3*x^4/4! - x^6/6! - 77*x^8/8! + ...

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

Cf. A213066, A213067, A213068.

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 *)

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

cp's OEIS Frontend

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

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