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.
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, 2302, 1351, 351, 36, 1, 0, 1, 88, 2159, 14859, 40319, 49434, 29378, 8627, 1222, 72, 1, 0, 1, 183, 9052, 113919, 554030, 1236040, 1380913, 816404, 260968, 44577, 3851, 141, 1
Offset: 0
Examples
Triangle starts: [0] [1] [1] [0, 1] [2] [0, 1, 2, 1] [3] [0, 1, 7, 14, 7, 1] [4] [0, 1, 18, 94, 145, 84, 17, 1] [5] [0, 1, 41, 481, 1676, 2302, 1351, 351, 36, 1] [6] [0, 1, 88, 2159, 14859, 40319, 49434, 29378, 8627, 1222, 72, 1]
Programs
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Maple
PolyProd(Stirling2, combinat:-eulerian1, 7); # Using PolyProd from A373657.