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A012324 arctanh(arcsin(x)*exp(x))=x+2/2!*x^2+6/3!*x^3+32/4!*x^4+248/5!*x^5... 0

%I #11 Feb 05 2015 07:51:30

%S 0,1,2,6,32,248,2240,24584,314176,4604864,75708928,1384714496,

%T 27844334080,610980624512,14521108083456,371703786041600,

%U 10193800681881600,298204898039689216,9268641663992807424

%N arctanh(arcsin(x)*exp(x))=x+2/2!*x^2+6/3!*x^3+32/4!*x^4+248/5!*x^5...

%F a(n) ~ (n-1)! / (2 * r^n), where r = 0.546947494527286418832891321710111770819... is the root of the equation arcsin(r)*exp(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015

%t With[{nn=20},CoefficientList[Series[ArcTanh[ArcSin[x]Exp[x]],{x,0,nn}], x]Range[0,nn]!] (* _Harvey P. Dale_, Feb 02 2012 *)

%K nonn

%O 0,3

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

%E Prepended missing a(0)=0 from _Vaclav Kotesovec_, Feb 05 2015

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Last modified February 23 14:24 EST 2024. Contains 370283 sequences. (Running on oeis4.)