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A373427
Triangle read by rows: Coefficients of the polynomials SC(n, x) * EZ(n, x), where SC denote the Stirling cycle polynomials and EZ the Eulerian zig-zag polynomials A205497.
1
1, 0, 1, 0, 1, 1, 0, 2, 5, 4, 1, 0, 6, 29, 45, 30, 9, 1, 0, 24, 218, 553, 629, 366, 112, 17, 1, 0, 120, 1954, 7781, 13409, 12136, 6270, 1894, 326, 29, 1, 0, 720, 20484, 125968, 313715, 407297, 308286, 143725, 42124, 7683, 830, 47, 1
OFFSET
0,8
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, 2, 3, 1] = [0, 2, 5, 4, 1]
4: [1, 3, 1] * [0, 6, 11, 6, 1] = [0, 6, 29, 45, 30, 9, 1]
5: [1, 7, 7, 1] * [0, 24, 50, 35, 10, 1] = [0, 24, 218, 553, 629, 366, 112,17,1]
MAPLE
EZP((n, k) -> abs(Stirling1(n, k)), 7); # Using function EZP from A373432.
CROSSREFS
Cf. A132393 (Stirling cycle), A205497 (zig-zag Eulerian), A373433 (row sums).
Sequence in context: A106315 A285295 A217563 * A254881 A100946 A377311
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Jun 07 2024
STATUS
approved