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%I #15 Nov 03 2018 19:05:08
%S 1,1,-3,1,1,-1,-1,-1,1,1,-1,0,-1,0,-1,1,1,-1,0,0,-1,0,0,-1,1,1,-1,0,0,
%T 0,-1,0,0,0,-1,1,1,-1,0,0,0,0,-1,0,0,0,0,-1,1,1,-1,0,0,0,0,0,-1,0,0,0,
%U 0,0,-1,1,1,-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,0,0,0
%N Triangle T(n,m) with the coefficient [x^m] of the polynomial x^(2*n) - x^(2*n - 1) - x^n - x + 1 in row n, column m, 1 <= m <= 2*n. T(0,0) = 1.
%C The polynomials up to n = 10 are Salem polynomials (the third lowest Salem in the table).
%H Michael Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>
%H William J. Floyd, <a href="http://dx.doi.org/10.1007/BF01444729">Growth of planar Coxeter groups, P.V. numbers, and Salem numbers</a>, Math. Ann. Vol. 293 (1992), 475-483.
%F Sum_{m=0..2*n} T(n,m)= -1.
%F From _Franck Maminirina Ramaharo_, Nov 02 2018: (Start)
%F G.f.: (1 - 4*x*y + x*(2 + x + 2*x^2)*y^2 - x^2*(1 + x^2)*y^3)/((1 - y)*(1 - x*y)*(1 - x^2*y)).
%F E.g.f.: (-(1 - x)*exp(x^2*y) - x*exp(x*y) + x*(1 - x)*exp(y) + 1 + x^2)/x. (End)
%e The polynomial coefficients are
%e 1;
%e 1, -3, 1;
%e 1, -1, -1, -1, 1;
%e 1, -1, 0, -1, 0, -1, 1;
%e 1, -1, 0, 0, -1, 0, 0, -1, 1;
%e 1, -1, 0, 0, 0, -1, 0, 0, 0, -1, 1;
%e 1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 1;
%e 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1;
%e 1, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 1;
%e 1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1;
%e 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1;
%e ...
%e The corresponding Mahler measures are
%e -----------------------------------------------------
%e n | M(p_n) || n | M(p_n)
%e -----------------------------------------------------
%e 1 | 1.7220838057390422450 || 6 | 1.2612309611
%e 2 | 1.5061356795538388 || 7 | 1.2363179318
%e 3 | 1.40126836793 || 8 | 1.21639166113826509
%e 4 | 1.337313210201 || 9 | 1.200026523
%e 5 | 1.293485953125 || 10 | 1.286735
%e ...
%t p[x_, n_] = If[n == 0, 1, x^(2*n) - x^(2*n - 1) - x^n - x + 1];
%t Table[CoefficientList[p[x, n], x], {n, 0, 10}]//Flatten
%o (Maxima) T(n, k) := if n = 0 and k = 0 then 1 else ratcoef(x^(2*n) - x^(2*n - 1) - x^n - x + 1, x, k)$
%o create_list(T(n, k), n, 0, 10, k, 0, 2*n); /* _Franck Maminirina Ramaharo_, Nov 02 2018 */
%Y Cf. A143439.
%K sign,easy,tabf
%O 0,3
%A _Roger L. Bagula_, Dec 04 2010