A373427 - OEIS

%I #8 Jun 13 2024 08:31:33

%S 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,

%T 0,120,1954,7781,13409,12136,6270,1894,326,29,1,0,720,20484,125968,

%U 313715,407297,308286,143725,42124,7683,830,47,1

%N 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.

%H Peter Luschny, <a href="/A373427/a373427.png">Illustrating the polynomials</a>.

%e Tracing the computation:

%e 0: [1] *          [1] =                    [1]

%e 1: [1] *          [0,  1] =                [0,  1]

%e 2: [1] *          [0,  1, 1] =             [0,  1,   1]

%e 3: [1, 1] *       [0,  2, 3, 1] =          [0,  2,   5,   4,   1]

%e 4: [1, 3, 1] *    [0,  6, 11, 6, 1] =      [0,  6,  29,  45,  30,   9,   1]

%e 5: [1, 7, 7, 1] * [0, 24, 50, 35, 10, 1] = [0, 24, 218, 553, 629, 366, 112,17,1]

%p EZP((n, k) -> abs(Stirling1(n, k)), 7);  # Using function EZP from A373432.

%Y Cf. A132393 (Stirling cycle), A205497 (zig-zag Eulerian), A373433 (row sums).

%Y Cf. A373429, A373428, A373432.

%K nonn,tabf

%O 0,8

%A _Peter Luschny_, Jun 07 2024