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.

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

Author

Peter Luschny, Jun 16 2024

Keywords

• nonn
• tabf

Examples

			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]
		

Crossrefs

Cf. A173018, A132393, A000142, A373657, A001044 (row sums).

Programs

Maple

PolyProd(((n, k) -> abs(Stirling1(n, k))), combinat:-eulerian1, 7); # Using PolyProd from A373657.