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A373572
Triangle read by rows: Coefficients of the polynomials P(n, x) * EZ(n, x), where P denote the signed Pascal polynomials and EZ the Eulerian zig-zag polynomials A205497.
0
1, -1, 1, 1, -2, 1, -1, 2, 0, -2, 1, 1, -1, -5, 10, -5, -1, 1, -1, -2, 18, -26, 0, 26, -18, 2, 1, 1, 8, -38, 18, 117, -212, 117, 18, -38, 8, 1, -1, -19, 52, 143, -677, 818, 0, -818, 677, -143, -52, 19, 1, 1, 38, -6, -817, 2196, -722, -5071, 8762, -5071, -722, 2196, -817, -6, 38, 1
OFFSET
0,5
EXAMPLE
Triangle starts:
[0] [1]
[1] [-1, 1]
[2] [ 1, -2, 1]
[3] [-1, 2, 0, -2, 1]
[4] [ 1, -1, -5, 10, -5, -1, 1]
[5] [-1, -2, 18, -26, 0, 26, -18, 2, 1]
[6] [ 1, 8, -38, 18, 117, -212, 117, 18, -38, 8, 1]
[7] [-1, -19, 52, 143, -677, 818, 0, -818, 677, -143, -52, 19, 1]
MAPLE
EZP((n, k) -> (-1)^(n-k)*binomial(n, k), 8); # Using function EZP from A373432.
CROSSREFS
Cf. A373432, A205497, A373657, A000007 (row sums).
Sequence in context: A089062 A282634 A039980 * A306660 A357332 A347367
KEYWORD
sign,tabf
AUTHOR
Peter Luschny, Jun 15 2024
STATUS
approved