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Search: id:A135685
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| A135685 |
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Triangular sequence of the coefficients of the Numerator of the rational recursive sequence for Tan(n*y) with x=tan(y). |
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+0
1
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| 1, 0, 1, 0, -2, 0, -3, 0, 1, 0, 4, 0, -4, 0, 5, 0, -10, 0, 1, 0, -6, 0, 20, 0, -6, 0, -7, 0, 35, 0, -21, 0, 1, 0, 8, 0, -56, 0, 56, 0, -8, 0, 9, 0, -84, 0, 126, 0, -36, 0, 1, 0, -10, 0, 120, 0, -252, 0, 120, 0, -10, 0, -11, 0, 165, 0, -462, 0, 330, 0, -55, 0, 1
(list; graph; listen)
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OFFSET
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1,5
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FORMULA
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p(x,0)=1;p(x,1)=x;p(x, n) = (p(x, n - 1) + x)/(1 - p(x, n - 1)*x);
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EXAMPLE
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{1},
{0, 1},
{0, -2},
{0, -3, 0,1},
{0, 4, 0, -4},
{0, 5, 0, -10, 0, 1},
{0, -6, 0, 20, 0, -6},
{0, -7, 0, 35, 0, -21, 0,1},
{0, 8, 0, -56, 0, 56, 0, -8},
{0, 9, 0, -84, 0, 126, 0, -36, 0, 1},
{0, -10, 0, 120, 0, -252, 0, 120,0, -10},
{0, -11, 0, 165, 0, -462, 0, 330, 0, -55, 0, 1}
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MATHEMATICA
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Clear[p, x, a, b] p[x, 0] = 1; p[x, 1] = x; p[x, 2] = 2*x/(1 - x^2); p[x, 3] = (3*x - x^3)/(1 - 3*x^2); p[x_, n_] := p[x, n] = (p[x, n - 1] + x)/(1 - p[x, n - 1]*x); c = Table[CoefficientList[Numerator[FullSimplify[p[x, n]]], x], {n, 0, 11}]; Flatten[c]
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CROSSREFS
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Adjacent sequences: A135682 A135683 A135684 this_sequence A135686 A135687 A135688
Sequence in context: A113290 A078442 A135523 this_sequence A079067 A065134 A088673
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KEYWORD
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uned,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 17 2008
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