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.

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

Author

Peter Luschny, Jun 15 2024

Keywords

• sign
• tabf

Examples

			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]
		

Crossrefs

Cf. A373432, A205497, A373657, A000007 (row sums).

Programs

Maple

EZP((n, k) -> (-1)^(n-k)*binomial(n, k), 8);  # Using function EZP from A373432.