login
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.
0

%I #5 Jun 16 2024 04:46:56

%S 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 2302,1351,351,36,1,0,1,88,2159,14859,40319,49434,29378,8627,1222,72,

%U 1,0,1,183,9052,113919,554030,1236040,1380913,816404,260968,44577,3851,141,1

%N 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 Triangle starts:

%e [0] [1]

%e [1] [0, 1]

%e [2] [0, 1, 2, 1]

%e [3] [0, 1, 7, 14, 7, 1]

%e [4] [0, 1, 18, 94, 145, 84, 17, 1]

%e [5] [0, 1, 41, 481, 1676, 2302, 1351, 351, 36, 1]

%e [6] [0, 1, 88, 2159, 14859, 40319, 49434, 29378, 8627, 1222, 72, 1]

%p PolyProd(Stirling2, combinat:-eulerian1, 7); # Using PolyProd from A373657.

%Y Cf. A048993, A173018, A373657, A373428, A320956, A137341 (row sums).

%K nonn,tabf

%O 0,6

%A _Peter Luschny_, Jun 15 2024