A012613 - OEIS

%I #11 Sep 30 2025 20:34:16

%S 0,2,4,350,7208,1278298,79874540,24248146806,3094746649296,

%T 1450703467495218,311518889830786132,210537148539150077966,

%U 67821849231894539132920,62959878878133692157576586

%N tan(arcsinh(x)*tan(x))=2/2!*x^2+4/4!*x^4+350/6!*x^6+7208/8!*x^8...

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

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

%K nonn

%O 0,2

%A _Patrick Demichel_

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