A373428 Triangle read by rows: Coefficients of the polynomials S2(n, x) * EZ(n, x), where S2 denote the Stirling set polynomials and EZ the Eulerian zig-zag polynomials A205497.

1, 0, 1, 0, 1, 1, 0, 1, 4, 4, 1, 0, 1, 10, 28, 26, 9, 1, 0, 1, 22, 137, 291, 261, 102, 17, 1, 0, 1, 45, 555, 2300, 4150, 3517, 1479, 306, 29, 1, 0, 1, 89, 2048, 15152, 48942, 76259, 61846, 26976, 6388, 795, 47, 1

Offset: 0

Author

Peter Luschny, Jun 06 2024

Keywords

• nonn
• tabf

Examples

			Tracing the computation:
0: [1] *          [1] =                   [1]
1: [1] *          [0, 1] =                [0, 1]
2: [1] *          [0, 1, 1] =             [0, 1, 1]
3: [1, 1] *       [0, 1, 3, 1] =          [0, 1, 4, 4, 1]
4: [1, 3, 1] *    [0, 1, 7, 6, 1] =       [0, 1, 10, 28, 26, 9, 1]
5: [1, 7, 7, 1] * [0, 1, 15, 25, 10, 1] = [0, 1, 22, 137, 291, 261, 102, 17, 1]
		

Links

• Peter Luschny, Illustrating the polynomials.

Crossrefs

Cf. A048993 (Stirling2), A205497 (zig-zag Eulerian), A320956 (row sums).

Programs

Maple

EZP(Stirling2, 7);  # Using function EZP from A373432.