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A135670 Triangular sequence of the coefficients of the denominator of the rational recursive sequence for tan(n*x). 4
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; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..71.

Clark Kimberling, Polynomials associated with reciprocation, JIS 12 (2009) 09.3.4, section 5.

EXAMPLE

{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}

MATHEMATICA

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]

CROSSREFS

Sequence in context: A175779 A280819 A300280 * A096754 A021767 A071417

Adjacent sequences:  A135667 A135668 A135669 * A135671 A135672 A135673

KEYWORD

sign,frac

AUTHOR

Roger L. Bagula, Feb 17 2008

EXTENSIONS

Edited by the Associate Editors of the OEIS, Aug 18 2009

STATUS

approved

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Last modified May 7 06:56 EDT 2021. Contains 343636 sequences. (Running on oeis4.)