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A373571 Triangle read by rows: Coefficients of the polynomials S2(n, x) * EP(n, x), where S2 denote the Stirling set polynomials and EP the Eulerian polynomials A173018.

%I A373571 #5 Jun 16 2024 04:46:56
%S A373571 1,0,1,0,1,2,1,0,1,7,14,7,1,0,1,18,94,145,84,17,1,0,1,41,481,1676,
%T A373571 2302,1351,351,36,1,0,1,88,2159,14859,40319,49434,29378,8627,1222,72,
%U A373571 1,0,1,183,9052,113919,554030,1236040,1380913,816404,260968,44577,3851,141,1
%N A373571 Triangle read by rows: Coefficients of the polynomials S2(n, x) * EP(n, x), where S2 denote the Stirling set polynomials and EP the Eulerian polynomials A173018.
%e A373571 Triangle starts:
%e A373571 [0] [1]
%e A373571 [1] [0, 1]
%e A373571 [2] [0, 1,  2,    1]
%e A373571 [3] [0, 1,  7,   14,     7,     1]
%e A373571 [4] [0, 1, 18,   94,   145,    84,    17,     1]
%e A373571 [5] [0, 1, 41,  481,  1676,  2302,  1351,   351,   36,    1]
%e A373571 [6] [0, 1, 88, 2159, 14859, 40319, 49434, 29378, 8627, 1222, 72, 1]
%p A373571 PolyProd(Stirling2, combinat:-eulerian1, 7);  # Using PolyProd from A373657.
%Y A373571 Cf. A048993, A173018, A373657, A373428, A320956, A137341 (row sums).
%K A373571 nonn,tabf
%O A373571 0,6
%A A373571 _Peter Luschny_, Jun 15 2024