A012039 - OEIS

%I #10 Mar 18 2023 16:51:34

%S 1,-1,1,111,-9407,957791,-131065791,23876150351,-5645293077119,

%T 1689130316350143,-625455343415905919,281176376077651011119,

%U -150982531394396522439999,95493861079696805301099551

%N sinh(sin(arcsinh(x))) = x-1/3!*x^3+1/5!*x^5+111/7!*x^7-9407/9!*x^9...

%F a(n) ~ (-1)^n * cos(sinh(Pi/2)) * cosh(Pi/2) * 2^(2*n+1) * n^(2*n) / exp(2*n). - _Vaclav Kotesovec_, Oct 30 2013

%t Table[n!*SeriesCoefficient[Sinh[Sin[ArcSinh[x]]],{x,0,n}],{n,1,40,2}] (* _Vaclav Kotesovec_, Oct 30 2013 *)

%t With[{nn=30},Take[CoefficientList[Series[Sinh[Sin[ArcSinh[x]]],{x,0,nn}],x] Range[ 0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Mar 18 2023 *)

%K sign

%O 0,4

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