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Search: id:A135670
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| A135670 |
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Triangular sequence of the coefficients of the denominator of the rational recursive sequence for tan(n*x). |
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+0
5
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| 1, 1, -1, 0, 1, -1, 0, 3, 1, 0, -6, 0, 1, 1, 0, -10, 0, 5, -1, 0, 15, 0, -15, 0, 1, -1, 0, 21, 0, -35, 0, 7, 1, 0, -28, 0, 70, 0, -28, 0, 1, 1, 0, -36, 0, 126, 0, -84, 0, 9, -1, 0, 45, 0, -210, 0, 210, 0, -45, 0, 1, -1, 0, 55, 0, -330, 0, 462, 0, -165, 0, 11
(list; graph; listen)
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OFFSET
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0,8
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COMMENT
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These are the denominators of the expansion of tan(n*x) as in A034839, but keeping the
zeros with the terms in the denominator polynomials that vanish. Sign conventions differ
slightly, maintaining either a positive coefficient [x^0], or a positive coefficient [x^n] or [x^(n-1)], resp.
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EXAMPLE
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{1},
{1},
{-1, 0, 1},
{-1, 0, 3},
{1, 0, -6,0, 1},
{1, 0, -10, 0, 5},
{-1, 0, 15, 0, -15, 0, 1},
{-1, 0, 21, 0, -35, 0, 7},
{1, 0, -28, 0, 70, 0, -28, 0, 1},
{1, 0, -36,0, 126, 0, -84, 0, 9},
{-1, 0, 45, 0, -210, 0, 210, 0, -45, 0, 1},
{-1, 0, 55, 0, -330, 0, 462, 0, -165, 0, 11}
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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[Denominator[FullSimplify[p[x, n]]], x], {n, 0, 11}]; Flatten[c]
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CROSSREFS
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Sequence in context: A011084 A021326 A110032 this_sequence A096754 A021767 A071417
Adjacent sequences: A135667 A135668 A135669 this_sequence A135671 A135672 A135673
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KEYWORD
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sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 17 2008
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EXTENSIONS
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Edited by the Associate Editors of the OEIS, Aug 18 2009
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