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, 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

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,  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).

Cf. A373429, A373428, A373432.

Sequence in context: A106315 A285295 A217563 * A254881 A100946 A200019

Adjacent sequences: A373424 A373425 A373426 * A373428 A373429 A373430

Keyword

nonn,tabf

Author

Peter Luschny, Jun 07 2024

Status

approved