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A012022
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Expansion of e.g.f.: arctan(sin(arctan(x))) (odd powers only).
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1
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1, -5, 129, -7965, 903105, -163451925, 43259364225, -15764670046125, 7571150452490625, -4634731528895593125, 3522824632122301130625, -3255279003622294051528125, 3593928024032353882700450625
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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*n+1)!*(-1)^n*Sum_{j=1..n+1} binomial((2*n-1)/2, n+1-j) /(2*j-1). - Vladimir Kruchinin, May 19 2011
E.g.f.: Sum_{n >= 0} a(n)*x^(2n+1)/(2n+1)! = arctan(sin(arctan(x))).
a(n) = (2*n+1)! * [x^(2*n+1)] arctan(sin(arctan(x))).
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MATHEMATICA
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With[{nn=30}, Take[CoefficientList[Series[ArcTan[Sin[ArcTan[x]]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Dec 11 2013 *)
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PROG
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(Maxima)
a(n):= ((2*n+1)!* (-1)^n *sum(binomial((2*n-1)/2, n+1-j)/(2*j-1), j, 1, n+1)); /* Vladimir Kruchinin, May 19 2011 */
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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Patrick Demichel (patrick.demichel(AT)hp.com)
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STATUS
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approved
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