A373570
Triangle read by rows: Coefficients of the polynomials S1(n, x) * EP(n, x), where S1 denote the unsigned Stirling cycle polynomials A132393 and EP the Eulerian polynomials A173018.
Original entry on oeis.org
1, 0, 1, 0, 1, 2, 1, 0, 2, 11, 15, 7, 1, 0, 6, 77, 193, 194, 88, 17, 1, 0, 24, 674, 2919, 4844, 3895, 1646, 361, 36, 1, 0, 120, 7114, 52083, 131898, 162398, 110214, 43356, 9902, 1242, 72, 1, 0, 720, 88164, 1070824, 4036059, 7141903, 7007314, 4133290, 1519960, 350176, 49162, 3886, 141, 1
Offset: 0
Triangle starts:
[0] [1]
[1] [0, 1]
[2] [0, 1, 2, 1]
[3] [0, 2, 11, 15, 7, 1]
[4] [0, 6, 77, 193, 194, 88, 17, 1]
[5] [0, 24, 674, 2919, 4844, 3895, 1646, 361, 36, 1]
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PolyProd(((n, k) -> abs(Stirling1(n, k))), combinat:-eulerian1, 7); # Using PolyProd from A373657.
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.
Original entry on oeis.org
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
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]
A373572
Triangle read by rows: Coefficients of the polynomials P(n, x) * EZ(n, x), where P denote the signed Pascal polynomials and EZ the Eulerian zig-zag polynomials A205497.
Original entry on oeis.org
1, -1, 1, 1, -2, 1, -1, 2, 0, -2, 1, 1, -1, -5, 10, -5, -1, 1, -1, -2, 18, -26, 0, 26, -18, 2, 1, 1, 8, -38, 18, 117, -212, 117, 18, -38, 8, 1, -1, -19, 52, 143, -677, 818, 0, -818, 677, -143, -52, 19, 1, 1, 38, -6, -817, 2196, -722, -5071, 8762, -5071, -722, 2196, -817, -6, 38, 1
Offset: 0
Triangle starts:
[0] [1]
[1] [-1, 1]
[2] [ 1, -2, 1]
[3] [-1, 2, 0, -2, 1]
[4] [ 1, -1, -5, 10, -5, -1, 1]
[5] [-1, -2, 18, -26, 0, 26, -18, 2, 1]
[6] [ 1, 8, -38, 18, 117, -212, 117, 18, -38, 8, 1]
[7] [-1, -19, 52, 143, -677, 818, 0, -818, 677, -143, -52, 19, 1]
Showing 1-3 of 3 results.