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

0,6

Links

Table of n, a(n) for n=0..56.

Example

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]

Maple

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

Crossrefs

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

Sequence in context: A339780 A199469 A266832 * A307772 A225203 A136255

Adjacent sequences: A373567 A373568 A373569 * A373571 A373572 A373573

Keyword

nonn,tabf

Author

Peter Luschny, Jun 16 2024

Status

approved