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 A012022 E.g.f.: arctan(sin(arctan(x))) (odd powers only). 0
 1, -5, 129, -7965, 903105, -163451925, 43259364225, -15764670046125, 7571150452490625, -4634731528895593125, 3522824632122301130625, -3255279003622294051528125, 3593928024032353882700450625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(n) = ((2*n+1)!*(-1)^n*sum(j=1..n+1, binomial((2*n-1)/2,n+1-j) /(2*j-1))).  [From Vladimir Kruchinin, May 19 2011] E.g.f.: sum(a(n) x^(2n+1)/(2n+1)! = arctan(sin(arctan(x))). a(n) = (2*n+1)! * [x^(2*n+1)] arctan(sin(arctan(x))). EXAMPLE atan(sin(atan(x))) = x - 5/6*x^3 + 43/40*x^5 -+... MATHEMATICA 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 *) PROG (Maxima) a(n):= ((2*n+1)!* (-1)^n *sum(binomial((2*n-1)/2, n+1-j)/(2*j-1), j, 1, n+1)); [From Vladimir Kruchinin, May 19 2011] CROSSREFS Sequence in context: A094074 A012218 A012136 * A012176 A012187 A012083 Adjacent sequences:  A012019 A012020 A012021 * A012023 A012024 A012025 KEYWORD sign AUTHOR Patrick Demichel (patrick.demichel(AT)hp.com) STATUS approved

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