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A143439
Triangle whose n-th row is the expansion of x*(x^n*(x - 1) + (-1)^n*2).
1
-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, 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, 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
OFFSET
-1,7
LINKS
Eriko Hironaka, Salem-Boyd sequences and Hopf plumbing, Osaka J. Math. Volume 43, Number 3 (2006), 497-516.
Eriko Hironaka, Salem-Boyd sequences and Hopf plumbing, arXiv:math/0506602 [math.GT], 2005.
FORMULA
Sum_{k=0..n+2} = 2*A033999(n+2).
EXAMPLE
Triangle begins:
-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, 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, 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;
...
MATHEMATICA
p[x_, n_] = x*(x^n*(x - 1) + (-1)^n*2);
Table[CoefficientList[p[x, n], x], {n, -1, 10}]//Flatten
PROG
(Maxima) T(n, k) := ratcoef(x*(x^n*(x - 1) + (-1)^n*2), x, k)$
create_list(T(n, k), n, -1, 10, k, 0, n + 2); /* Franck Maminirina Ramaharo, Nov 02 2018 */
CROSSREFS
Cf. A175739.
Sequence in context: A362899 A168261 A180997 * A105469 A257857 A339871
KEYWORD
sign,tabf
AUTHOR
EXTENSIONS
Edited name, Joerg Arndt, May 26 2013
Offset corrected by Michel Marcus, May 27 2013
STATUS
approved