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A239608
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Sin( arcsin(n)- 2*arccos(n) )^2.
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4
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0, 1, 676, 9801, 59536, 235225, 715716, 1825201, 4096576, 8346321, 15760900, 27994681, 47279376, 76545001, 119552356, 181037025, 266864896, 384199201, 541679076, 749609641, 1020163600, 1367594361, 1808460676, 2361862801, 3049690176, 3896880625, 4931691076
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OFFSET
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0,3
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COMMENTS
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The terms are integers.
This is assuming the "standard branch" of arcsin and arccos, where sin(arccos(n)) = cos(arcsin(n)) = sqrt(1-n^2). - Robert Israel, May 25 2014
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LINKS
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FORMULA
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a(n) = n^2*(3-4*n^2)^2. G.f.: -x*(x+1)*(x^4+668*x^3+4422*x^2+668*x+1) / (x-1)^7. - Colin Barker, May 24 2014
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MATHEMATICA
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G[n_, a_, b_] := G[n, a, b] = Sin[a ArcSin[ n] + b ArcCos[n]]^2 // ComplexExpand // FullSimplify; Table[G[n, 1, -2], {n, 0, 43}]
CoefficientList[Series[- x (x + 1) (x^4 + 668 x^3 + 4422 x^2 + 668 x + 1)/(x - 1)^7, {x, 0, 50}], x] (* Vincenzo Librandi, May 30 2014 *)
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PROG
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(PARI) vector(100, n, round(sin(asin(n-1) - 2*acos(n-1))^2)) \\ Colin Barker, May 24 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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