A350269 Triangle read by rows, T(n, k) = (n - k)!*(n - 1)^k, for 0 <= k <= n.

1, 1, 0, 2, 1, 1, 6, 4, 4, 8, 24, 18, 18, 27, 81, 120, 96, 96, 128, 256, 1024, 720, 600, 600, 750, 1250, 3125, 15625, 5040, 4320, 4320, 5184, 7776, 15552, 46656, 279936, 40320, 35280, 35280, 41160, 57624, 100842, 235298, 823543, 5764801

Offset: 0

Author

Peter Luschny, Dec 25 2021

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0]     1
[1]     1,     0
[2]     2,     1,     1
[3]     6,     4,     4,     8
[4]    24,    18,    18,    27,    81
[5]   120,    96,    96,   128,   256,   1024
[6]   720,   600,   600,   750,  1250,   3125,  15625
[7]  5040,  4320,  4320,  5184,  7776,  15552,  46656, 279936
[8] 40320, 35280, 35280, 41160, 57624, 100842, 235298, 823543, 5764801
		

Crossrefs

Cf. A000142 (first column), A001563 (second column), A000312 (subdiagonal), A065440 (main diagonal), A350268 (row sums).

Programs

Maple

A350269 := (n, k) -> (n - k)!*(n - 1)^k:
seq(seq(A350269(n, k), k = 0..n), n = 0..9);

Mathematica

T[n_, k_] := If[n - 1 == k == 0, 1, (n - k)! * (n - 1)^k]; Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Amiram Eldar, Dec 25 2021 *)