A373426 Triangle read by rows: Coefficients of the polynomials L(n, x) * EZ(n, x), where L denote the unsigned Lah polynomials and EZ the Eulerian zig-zag polynomials A205497.

1, 0, 1, 0, 2, 1, 0, 6, 12, 7, 1, 0, 24, 108, 144, 73, 15, 1, 0, 120, 1080, 2640, 2660, 1221, 267, 27, 1, 0, 720, 11880, 48720, 82980, 67350, 28321, 6344, 751, 44, 1, 0, 5040, 146160, 955080, 2529240, 3262350, 2245782, 870283, 195074, 25267, 1831, 68, 1

Offset: 0

Author

Peter Luschny, Jun 07 2024

Keywords

• nonn
• tabf

Examples

			Tracing the computation:
  0: [1] *       [1] =                [1]
  1: [1] *       [0,  1] =            [0,  1]
  2: [1] *       [0,  2,  1] =        [0,  2,   1]
  3: [1, 1] *    [0,  6,  6,  1] =    [0,  6,  12,   7,  1]
  4: [1, 3, 1] * [0, 24, 36, 12, 1] = [0, 24, 108, 144, 73, 15, 1]
		

Links

• Peter Luschny, Illustrating the polynomials.

Crossrefs

Cf. A271703 (Lah), A205497 (zig-zag Eulerian), A373425 (row sums).

Programs

Maple

# Using function EZP from A373432.
EZP((n, k) -> ifelse(n=k, 1, binomial(n-1, k-1)*n!/k!), 7);