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%I #6 Nov 02 2014 12:18:36
%S -1,1,-1,0,1,-2,2,-2,2,-3,2,0,-2,3,-5,5,-6,6,-5,5,-8,8,-8,0,8,-8,8,
%T -13,15,-21,15,-15,21,-15,13,-21,26,-38,18,0,-18,38,-26,21,-34,46,-76,
%U 52,-48,48,-52,76,-46,34,-55,80,-141,96,-70,0,70,-96,141,-80
%N Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(n)*x^n which is the denominator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 1)/(x - 1).
%C Sum of numbers in row n: 0. Left and right edges: A000045 (Fibonacci numbers).
%e First 5 rows:
%e -1 . . . 1
%e -1 . . . 0 . . . 1
%e -2 . . . 2 . . . -2 . . . 2
%e -3 . . . 2 . . . 0 . . . -2 . . . 3
%e -5 . . . 5 . . . -6 . . . 6 . . . -5 . . . 5
%e First 3 polynomials: -1 + x, -1 + x^2, -2 + 2*x - 2*x^2 + 2*x^3.
%t t[n_] := t[n] = Table[(x + 1)/(x - 1), {k, 0, n}];
%t b = Table[Factor[Convergents[t[n]]], {n, 0, 10}];
%t p[x_, n_] := p[x, n] = Last[Expand[Denominator[b]]][[n]];
%t u = Table[p[x, n], {n, 1, 10}]
%t v = CoefficientList[u, x]; Flatten[v]
%Y Cf. A230000, A000045, A231154.
%K sign,tabf
%O 1,6
%A _Clark Kimberling_, Nov 13 2013
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