%I #8 Feb 09 2023 05:53:55

%S 1,0,2,0,2,3,0,4,9,4,0,12,33,24,5,0,48,150,140,50,6,0,240,822,900,425,

%T 90,7,0,1440,5292,6496,3675,1050,147,8,0,10080,39204,52528,33845,

%U 11760,2254,224,9,0,80640,328752,472496,336420,134694,31752,4368,324,10

%N Triangle read by rows. T(n, k) = (k + 1) * abs(Stirling1(n, k)).

%e Triangle T(n, k) starts:

%e [0] 1;

%e [1] 0, 2;

%e [2] 0, 2, 3;

%e [3] 0, 4, 9, 4;

%e [4] 0, 12, 33, 24, 5;

%e [5] 0, 48, 150, 140, 50, 6;

%e [6] 0, 240, 822, 900, 425, 90, 7;

%e [7] 0, 1440, 5292, 6496, 3675, 1050, 147, 8;

%e [8] 0, 10080, 39204, 52528, 33845, 11760, 2254, 224, 9;

%p T := (n, k) -> (k + 1)*abs(Stirling1(n, k)):

%p for n from 0 to 8 do seq(T(n, k), k = 0..n) od;

%Y Cf. A208529 (column 1), A006002 (subdiagonal), A000774 (row sums).

%Y Cf. A069138 (Stirling2 counterpart), A360205 (Lah counterpart).

%K nonn,tabl

%O 0,3

%A _Peter Luschny_, Feb 08 2023