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

0,9

Links

Table of n, a(n) for n=0..50.

Peter Luschny, Illustrating the polynomials.

Example

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]

Maple

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

Crossrefs

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

Sequence in context: A350037 A070430 A336302 * A163353 A164612 A309748

Adjacent sequences: A373425 A373426 A373427 * A373429 A373430 A373431

Keyword

nonn,tabf

Author

Peter Luschny, Jun 06 2024

Status

approved