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A263848
Irregular triangle read by rows: row n gives coefficients of basis polynomial {n,k} expressed in terms of binomial coefficients, high order terms first.
2
1, 1, -1, 1, 0, -1, 1, -1, 1, 1, 0, 0, -1, 2, 0, -1, 1, 2, -1, 0, 1, 1, -1, 1, -1, 1, 0, 0, 0, -1, 3, 0, 0, -1, 1, 5, 0, -1, 0, 1, 3, 0, -1, 1, -1, 3, -1, 0, 0, 1, 5, -2, 0, 1, -1, 3, -2, 1, 0, -1, 1, -1, 1, -1, 1, 1, 0, 0, 0, 0, -1, 4, 0, 0, 0, -1, 1, 9, 0, 0
OFFSET
0,14
LINKS
Peter J. C. Moses, First 300 rows.
Vladimir Shevelev, On the Basis Polynomials in the Theory of Permutations with Prescribed Up-Down Structure, arXiv|math.CO/0801.0072, 2007-2010. See Appendix.
V. Shevelev and J. Spilker, Up-down coefficients for permutations, Elemente der Mathematik, Vol. 68 (2013), no. 3, 115-127.
EXAMPLE
Triangle begins:
1,
1, -1,
1, 0, -1,
1, -1, 1,
1, 0, 0, -1,
2, 0, -1, 1,
2, -1, 0, 1,
1, -1, 1, -1,
1, 0, 0, 0, -1,
3, 0, 0, -1, 1,
...
CROSSREFS
Sequence in context: A334296 A227003 A307431 * A348157 A108455 A193759
KEYWORD
sign,tabf,more
AUTHOR
N. J. A. Sloane, Nov 15 2015
EXTENSIONS
More terms from Peter J. C. Moses, Dec 12 2015
STATUS
approved