

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
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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^(n1)], 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



