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A012251 exp(arcsinh(arctan(x)))=1+x+1/2!*x^2-2/3!*x^3-11/4!*x^4+24/5!*x^5... 2

%I #11 Dec 21 2013 22:36:43

%S 1,1,1,-2,-11,24,349,-720,-22455,40320,2465241,-3628800,-416217603,

%T 479001600,100729124469,-87178291200,-33198564667887,20922789888000,

%U 14328891118054449,-6402373705728000,-7852649782447649403

%N exp(arcsinh(arctan(x)))=1+x+1/2!*x^2-2/3!*x^3-11/4!*x^4+24/5!*x^5...

%F E.g.f.: Q(0)-1, where Q(k) = 2 + arctan(x)/(1 - arctan(x)/Q(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Dec 19 2013

%t With[{nn=30},CoefficientList[Series[Exp[ArcSinh[ArcTan[x]]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 26 2011 *)

%Y Bisections are (-1)^n*A010050 and (-1)^n*A012138.

%K sign

%O 0,4

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

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Last modified February 22 06:21 EST 2024. Contains 370240 sequences. (Running on oeis4.)