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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.
5
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
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
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Jun 06 2024
STATUS
approved