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
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
KEYWORD
sign,frac
AUTHOR
Roger L. Bagula, Feb 17 2008
EXTENSIONS
Edited by the Associate Editors of the OEIS, Aug 18 2009
STATUS
approved