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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.
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%I #3 Jun 16 2024 04:46:50

%S 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,

%T 4844,3895,1646,361,36,1,0,120,7114,52083,131898,162398,110214,43356,

%U 9902,1242,72,1,0,720,88164,1070824,4036059,7141903,7007314,4133290,1519960,350176,49162,3886,141,1

%N 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.

%e Triangle starts:

%e [0] [1]

%e [1] [0, 1]

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

%e [3] [0, 2, 11, 15, 7, 1]

%e [4] [0, 6, 77, 193, 194, 88, 17, 1]

%e [5] [0, 24, 674, 2919, 4844, 3895, 1646, 361, 36, 1]

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

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

%K nonn,tabf

%O 0,6

%A _Peter Luschny_, Jun 16 2024