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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.

%I A373427 #8 Jun 13 2024 08:31:33
%S A373427 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 A373427 0,120,1954,7781,13409,12136,6270,1894,326,29,1,0,720,20484,125968,
%U A373427 313715,407297,308286,143725,42124,7683,830,47,1
%N 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.
%H A373427 Peter Luschny, <a href="/A373427/a373427.png">Illustrating the polynomials</a>.
%e A373427 Tracing the computation:
%e A373427 0: [1] *          [1] =                    [1]
%e A373427 1: [1] *          [0,  1] =                [0,  1]
%e A373427 2: [1] *          [0,  1, 1] =             [0,  1,   1]
%e A373427 3: [1, 1] *       [0,  2, 3, 1] =          [0,  2,   5,   4,   1]
%e A373427 4: [1, 3, 1] *    [0,  6, 11, 6, 1] =      [0,  6,  29,  45,  30,   9,   1]
%e A373427 5: [1, 7, 7, 1] * [0, 24, 50, 35, 10, 1] = [0, 24, 218, 553, 629, 366, 112,17,1]
%p A373427 EZP((n, k) -> abs(Stirling1(n, k)), 7);  # Using function EZP from A373432.
%Y A373427 Cf. A132393 (Stirling cycle), A205497 (zig-zag Eulerian), A373433 (row sums).
%Y A373427 Cf. A373429, A373428, A373432.
%K A373427 nonn,tabf
%O A373427 0,8
%A A373427 _Peter Luschny_, Jun 07 2024