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A012470 arcsinh(cos(x)*log(x+1))=x-1/2!*x^2-2/3!*x^3+6/4!*x^4+13/5!*x^5... 0

%I #8 Nov 02 2013 08:23:52

%S 0,1,-1,-2,6,13,-225,530,8540,-65579,-650565,13899070,-8281878,

%T -2388363655,18379145603,516826612354,-11083263907560,-64702488848279,

%U 5027641615912599,-24199820388513346

%N arcsinh(cos(x)*log(x+1))=x-1/2!*x^2-2/3!*x^3+6/4!*x^4+13/5!*x^5...

%F Lim sup n->infinity (|a(n)|/n!)^(1/n) = 1.25977488234489... = abs(1/r), where r is the complex root of the equation 1+r = exp(-I/cos(r)). - _Vaclav Kotesovec_, Nov 02 2013

%t CoefficientList[Series[ArcSinh[Cos[x]*Log[x+1]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 30 2013 *)

%K sign

%O 0,4

%A Patrick Demichel (patrick.demichel(AT)hp.com)

%E Prepended missing a(0)=0 from _Vaclav Kotesovec_, Nov 02 2013

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)