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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.

%I A373428 #6 Jun 13 2024 08:31:29
%S A373428 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,
%T A373428 1,45,555,2300,4150,3517,1479,306,29,1,0,1,89,2048,15152,48942,76259,
%U A373428 61846,26976,6388,795,47,1
%N 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.
%H A373428 Peter Luschny, <a href="/A373428/a373428.png">Illustrating the polynomials</a>.
%e A373428 Tracing the computation:
%e A373428 0: [1] *          [1] =                   [1]
%e A373428 1: [1] *          [0, 1] =                [0, 1]
%e A373428 2: [1] *          [0, 1, 1] =             [0, 1, 1]
%e A373428 3: [1, 1] *       [0, 1, 3, 1] =          [0, 1, 4, 4, 1]
%e A373428 4: [1, 3, 1] *    [0, 1, 7, 6, 1] =       [0, 1, 10, 28, 26, 9, 1]
%e A373428 5: [1, 7, 7, 1] * [0, 1, 15, 25, 10, 1] = [0, 1, 22, 137, 291, 261, 102, 17, 1]
%p A373428 EZP(Stirling2, 7);  # Using function EZP from A373432.
%Y A373428 Cf. A048993 (Stirling2), A205497 (zig-zag Eulerian), A320956 (row sums).
%K A373428 nonn,tabf
%O A373428 0,9
%A A373428 _Peter Luschny_, Jun 06 2024