%I #10 Feb 16 2025 15:52:33

%S 0,2,-8,8,2112,-199008,22569600,-3419806080,685509888000,

%T -177249701752320,57657923420313600,-23084838758992066560,

%U 11165823102677176074240,-6422018427189941047418880

%N sin(arcsinh(x)*arcsinh(x))=2/2!*x^2-8/4!*x^4+8/6!*x^6+2112/8!*x^8...

%F a(n) ~ (-1)^(n+1) * Pi * 2^(2*n) * n^(2*n-1) * cos((Pi^2)/4) / exp(2*n). - _Vaclav Kotesovec_, Nov 01 2013

%t Table[n!*SeriesCoefficient[Sin[ArcSinh[x]*ArcSinh[x]],{x,0,n}],{n,0,40,2}] (* _Vaclav Kotesovec_, Nov 01 2013 *)

%t With[{nn=30},Take[CoefficientList[Series[Sin[ArcSinh[x]^2],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Feb 16 2025 *)

%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