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A012536 tan(sinh(x)*arcsin(x))=2/2!*x^2+8/4!*x^4+320/6!*x^6+15808/8!*x^8... 0

%I #8 Feb 06 2015 10:15:01

%S 0,2,8,320,15808,1429888,189299200,34859305728,8524943044608,

%T 2667935751684096,1040196824976736256,494214397360327786496,

%U 281064144909266002903040,188495115535527543004266496

%N tan(sinh(x)*arcsin(x))=2/2!*x^2+8/4!*x^4+320/6!*x^6+15808/8!*x^8...

%F a(n) ~ 4 * (2*n)! / ((Pi/tanh(r) + 2*sinh(r)/sqrt(1-r^2)) * r^(2*n+1)), where r = 0.980280472307130556844984772871395757744942110943939753792691... is the root of the equation sinh(r)*arcsin(r) = Pi/2. - _Vaclav Kotesovec_, Feb 06 2015

%t nn = 20; Table[(CoefficientList[Series[Tan[ArcSin[x]*Sinh[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* _Vaclav Kotesovec_, Feb 06 2015 *)

%K nonn

%O 0,2

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

%E a(0)=0 prepended by _Vaclav Kotesovec_, Feb 06 2015

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Last modified February 23 09:02 EST 2024. Contains 370276 sequences. (Running on oeis4.)