A012611 - OEIS

%I #11 Jun 24 2015 13:54:34

%S 0,2,4,-10,-2872,-158102,-16416820,-978422562,-208568114544,

%T 49226001618,-7815364604207468,2061047671608594374,

%U -1093492387339592903336,671330623551827250908986,-418843222601740399516096420,353969402613094069055715957934

%N sin(arcsinh(x)*tan(x))=2/2!*x^2+4/4!*x^4-10/6!*x^6-2872/8!*x^8...

%F a(n) ~ (-1)^(n+1) * tanh(1) * cos(Pi*tanh(1)/2) * 2^(2*n) * n^(2*n-1) / exp(2*n). - _Vaclav Kotesovec_, Oct 31 2013

%t Table[n!*SeriesCoefficient[Sin[ArcSinh[x]*Tan[x]],{x,0,n}],{n,0,40,2}] (* _Vaclav Kotesovec_, Oct 31 2013 *)

%t With[{nn=30},Take[CoefficientList[Series[Sin[ArcSinh[x]Tan[x]],{x,0,nn}], x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Jun 24 2015 *)

%K sign

%O 0,2

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

%E Prepended missing a(0)=0, _Vaclav Kotesovec_, Oct 31 2013

%E More terms from _Harvey P. Dale_, Jun 24 2015