A263848 - OEIS

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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.

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

(list; graph; refs; listen; history; text; internal format)

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.

Vladimir Shevelev, The number of permutations with prescribed up-down structure as a function of two variables, INTEGERS, 12 (2012), #A1.

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, 0, -1,