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A012378
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tan(tan(x)*arcsin(x))=2/2!*x^2+12/4!*x^4+430/6!*x^6+26040/8!*x^8...
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1
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0, 2, 12, 430, 26040, 2661178, 402231940, 84456360742, 23476965450736, 8341678414816242, 3686586514781799292, 1982979948714026781726, 1275341677617693817452200, 966341800352400737116306986
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ 2 * (2*n)! / ((Pi/sin(2*r) + tan(r)/sqrt(1-r^2)) * r^(2*n+1)), where r = 0.925530521691094119047741289850... is the root of the equation tan(r)*arcsin(r) = Pi/2. - Vaclav Kotesovec, Feb 06 2015
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MATHEMATICA
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nn = 20; Table[(CoefficientList[Series[Tan[ArcSin[x]*Tan[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 06 2015 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Patrick Demichel (patrick.demichel(AT)hp.com)
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EXTENSIONS
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STATUS
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approved
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