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%I #13 Nov 03 2013 10:48:13
%S 0,2,-1,-7,18,243,-1785,-19086,308980,2736225,-90239805,-495769586,
%T 38522052690,39766893593,-22481798964989,111035038388104,
%U 16941789968380680,-219516343596465735,-15750892172912678361
%N arcsinh(sin(x)+log(x+1)) = 2*x-1/2!*x^2-7/3!*x^3+18/4!*x^4+243/5!*x^5...
%F Lim sup n->infinity (|a(n)|/n!)^(1/n) = 2.0027513568... = abs(1/r), where r is the complex root of the equation (r+1)*exp(sin(r)) = exp(I). - _Vaclav Kotesovec_, Nov 02 2013
%t CoefficientList[Series[ArcSinh[Sin[x]+Log[x+1]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Nov 01 2013 *)
%K sign
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Prepended missing a(0)=0 from _Vaclav Kotesovec_, Nov 01 2013