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E.g.f.: tanh(arcsinh(x)*tan(x)) = 2/2!*x^2+4/4!*x^4-130/6!*x^6-6232/8!*x^8...
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%I #16 Oct 30 2013 12:53:55

%S 2,4,-130,-6232,-32102,18014060,2634330582,-33133771824,

%T -37925465839182,-16267772522154668,2012491810909723310,

%U 52146402203293345912,867090565519403243923786,-388470254962420081890970180,207203200777273698360429465094

%N E.g.f.: tanh(arcsinh(x)*tan(x)) = 2/2!*x^2+4/4!*x^4-130/6!*x^6-6232/8!*x^8...

%H Alois P. Heinz, <a href="/A012617/b012617.txt">Table of n, a(n) for n = 1..100</a>

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

%p a:= n-> (2*n)! *coeff(series(tanh(arcsinh(x)*tan(x)), x, 2*n+2), x, 2*n):

%p seq (a(n), n=1..20); # _Alois P. Heinz_, Jul 11 2012

%t With[{nn=30},Take[CoefficientList[Series[Tanh[ArcSinh[x]Tan[x]],{x,0,nn}],x] Range[0,nn]!,{3,-1,2}]] (* _Harvey P. Dale_, Jul 11 2012 *)

%K sign

%O 1,1

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

%E Definition clarified by and more terms from _Harvey P. Dale_, Jul 11 2012