A012011 - OEIS

%I #14 Feb 03 2015 16:47:24

%S 1,-3,41,-1515,113489,-14321299,2716798969,-721988679547,

%T 255890614389921,-116619928299347491,66439023428917759945,

%U -46262911349611152912395,38656874720522348065089521

%N arcsinh(sin(sin(x)))=x-3/3!*x^3+41/5!*x^5-1515/7!*x^7+113489/9!*x^9...

%H Vaclav Kotesovec, <a href="/A012011/b012011.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) ~ (-1)^n * c * d^(2*n) * (2*n)! / sqrt(n), where d = 1 / arcsinh(arcsinh(1)) = 1.25792845770279367616342387910366384..., c = 0.8688030872074338111899369246534915... . - _Vaclav Kotesovec_, Feb 03 2015

%t Take[Rest[With[{nn=25},CoefficientList[Series[ArcSinh[Sin[Sin[x]]], {x,0,nn}], x]Range[0,nn]!]],{1,-1,2}] (* _Harvey P. Dale_, Oct 21 2011 *)

%K sign

%O 0,2

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

%E Confirmed by Harvey P. Dale, Oct 21 2011