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 A213069 Expansion of e.g.f. arcsinh(cos(x)*sech(x)), even powers only. 3

%I #17 Aug 19 2018 02:59:40

%S 0,-1,3,-1,-77,-13921,791043,23892959,-3518362637,-801110007361,

%T 149920222346883,24069808471917119,-7334638751184472397,

%U -2673575321959933341601,1059696929013386749787523,413637485668406346391368479

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

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

%H Vincenzo Librandi, <a href="/A213069/b213069.txt">Table of n, a(n) for n = 0..100</a>

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

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

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

%t 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 *)

%Y Cf. A213066, A213067, A213068.

%K sign

%O 0,3

%A _Olivier GĂ©rard_, Jun 04 2012

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Last modified August 4 22:06 EDT 2024. Contains 374934 sequences. (Running on oeis4.)