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 A135670 Triangular sequence of the coefficients of the denominator of the rational recursive sequence for tan(n*x). 5
 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 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 November 29 09:49 EST 2022. Contains 358423 sequences. (Running on oeis4.)