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%I #19 Nov 03 2018 18:59:57
%S -1,-1,0,1,1,0,-2,-1,1,0,2,0,-1,1,0,-2,0,0,-1,1,0,2,0,0,0,-1,1,0,-2,0,
%T 0,0,0,-1,1,0,2,0,0,0,0,0,-1,1,0,-2,0,0,0,0,0,0,-1,1,0,2,0,0,0,0,0,0,
%U 0,-1,1,0,-2,0,0,0,0,0,0,0,0,-1,1,0,2,0,0,0,0,0,0,0,0,0,-1,1
%N Triangle whose n-th row is the expansion of x*(x^n*(x - 1) + (-1)^n*2).
%H Eriko Hironaka, <a href="http://projecteuclid.org/euclid.ojm/1159189999">Salem-Boyd sequences and Hopf plumbing</a>, Osaka J. Math. Volume 43, Number 3 (2006), 497-516.
%H Eriko Hironaka, <a href="http://arxiv.org/abs/math/0506602v1">Salem-Boyd sequences and Hopf plumbing</a>, arXiv:math/0506602 [math.GT], 2005.
%F Sum_{k=0..n+2} = 2*A033999(n+2).
%e Triangle begins:
%e -1, -1;
%e 0, 1, 1;
%e 0, -2, -1, 1;
%e 0, 2, 0, -1, 1;
%e 0, -2, 0, 0, -1, 1;
%e 0, 2, 0, 0, 0, -1, 1;
%e 0, -2, 0, 0, 0, 0, -1, 1;
%e 0, 2, 0, 0, 0, 0, 0, -1, 1;
%e 0, -2, 0, 0, 0, 0, 0, 0, -1, 1;
%e 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 1;
%e 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1;
%e 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1;
%e ...
%t p[x_, n_] = x*(x^n*(x - 1) + (-1)^n*2);
%t Table[CoefficientList[p[x, n], x], {n, -1, 10}]//Flatten
%o (Maxima) T(n, k) := ratcoef(x*(x^n*(x - 1) + (-1)^n*2), x, k)$
%o create_list(T(n, k), n, -1, 10, k, 0, n + 2); /* _Franck Maminirina Ramaharo_, Nov 02 2018 */
%Y Cf. A175739.
%K sign,tabf
%O -1,7
%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 23 2008
%E Edited name, _Joerg Arndt_, May 26 2013
%E Offset corrected by _Michel Marcus_, May 27 2013
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