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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.

%I A373570 #3 Jun 16 2024 04:46:50
%S A373570 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 A373570 4844,3895,1646,361,36,1,0,120,7114,52083,131898,162398,110214,43356,
%U A373570 9902,1242,72,1,0,720,88164,1070824,4036059,7141903,7007314,4133290,1519960,350176,49162,3886,141,1
%N 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.
%e A373570 Triangle starts:
%e A373570 [0] [1]
%e A373570 [1] [0,  1]
%e A373570 [2] [0,  1,   2,    1]
%e A373570 [3] [0,  2,  11,   15,    7,    1]
%e A373570 [4] [0,  6,  77,  193,  194,   88,   17,   1]
%e A373570 [5] [0, 24, 674, 2919, 4844, 3895, 1646, 361, 36, 1]
%p A373570 PolyProd(((n, k) -> abs(Stirling1(n, k))), combinat:-eulerian1, 7); # Using PolyProd from A373657.
%Y A373570 Cf. A173018, A132393, A000142, A373657, A001044 (row sums).
%K A373570 nonn,tabf
%O A373570 0,6
%A A373570 _Peter Luschny_, Jun 16 2024