A355006 Triangle read by rows. T(n, k) = n^(n - k) * |Stirling1(n, k)|.
1, 0, 1, 0, 2, 1, 0, 18, 9, 1, 0, 384, 176, 24, 1, 0, 15000, 6250, 875, 50, 1, 0, 933120, 355104, 48600, 3060, 90, 1, 0, 84707280, 29647548, 3899224, 252105, 8575, 147, 1, 0, 10569646080, 3425697792, 430309376, 27725824, 1003520, 20608, 224, 1
Offset: 0
Examples
Table T(n, k) begins: [0] 1; [1] 0, 1; [2] 0, 2, 1; [3] 0, 18, 9, 1; [4] 0, 384, 176, 24, 1; [5] 0, 15000, 6250, 875, 50, 1; [6] 0, 933120, 355104, 48600, 3060, 90, 1; [7] 0, 84707280, 29647548, 3899224, 252105, 8575, 147, 1; [8] 0, 10569646080, 3425697792, 430309376, 27725824, 1003520, 20608, 224, 1;
Programs
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Maple
seq(seq(n^(n - k)*abs(Stirling1(n, k)), k = 0..n), n = 0..9);
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Mathematica
T[n_, k_] := If[n == k == 0, 1, n^(n - k) * Abs[StirlingS1[n, k]]]; Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Amiram Eldar, Jun 17 2022 *)