A369025 Triangle read by rows: T(n, k) = floor(binomial(n, k - 1) * (k - 1)^(k - 1) * k *(n - k + 1)^(n - k) / 2).

0, 0, 0, 0, 1, 2, 0, 4, 6, 18, 0, 32, 36, 72, 216, 0, 312, 320, 540, 1080, 3200, 0, 3888, 3750, 5760, 9720, 19200, 56250, 0, 58824, 54432, 78750, 120960, 201600, 393750, 1143072, 0, 1048576, 941192, 1306368, 1890000, 2867200, 4725000, 9144576, 26353376

Offset: 0

Author

Peter Luschny, Jan 12 2024

Keywords

• nonn
• tabl

Examples

			Triangle starts:
  [0] [0]
  [1] [0,     0]
  [2] [0,     1,     2]
  [3] [0,     4,     6,    18]
  [4] [0,    32,    36,    72,    216]
  [5] [0,   312,   320,   540,   1080,   3200]
  [6] [0,  3888,  3750,  5760,   9720,  19200,  56250]
  [7] [0, 58824, 54432, 78750, 120960, 201600, 393750, 1143072]
		

Crossrefs

Cf. A369026 (column 1), A369027 (main diagonal).

Programs

Mathematica

A369025[n_, k_] := Floor[Binomial[n, k-1] If[k == 1, 1, (k-1)^(k-1)] k (n-k+1)^(n-k) / 2];
Table[A369025[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Jan 12 2024 *)

SageMath

def A369025(n, k):
    return binomial(n, k-1)*(k-1)^(k-1)*k*(n-k+1)^(n-k)//2
for n in range(9): print([A369025(n, k) for k in range(n+1)])