A369072 Triangle read by rows: T(n, k) = floor(binomial(n, k - 1) * (k - 1)^(k - 1) * n * (n - k + 1)^(n - k) / 2).

0, 0, 0, 0, 2, 2, 0, 13, 9, 18, 0, 128, 72, 96, 216, 0, 1562, 800, 900, 1350, 3200, 0, 23328, 11250, 11520, 14580, 23040, 56250, 0, 411771, 190512, 183750, 211680, 282240, 459375, 1143072, 0, 8388608, 3764768, 3483648, 3780000, 4587520, 6300000, 10450944, 26353376

Offset: 0

Author

Peter Luschny, Jan 12 2024

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] [0]
[1] [0,      0]
[2] [0,      2,      2]
[3] [0,     13,      9,     18]
[4] [0,    128,     72,     96,    216]
[5] [0,   1562,    800,    900,   1350,   3200]
[6] [0,  23328,  11250,  11520,  14580,  23040,  56250]
[7] [0, 411771, 190512, 183750, 211680, 282240, 459375, 1143072]
		

Crossrefs

Cf. A057065 (column 1), A369027 (main diagonal).

Programs

Mathematica

A369072[n_, k_] := Floor[Binomial[n, k-1] If[k == 1, 1, (k-1)^(k-1)] n (n-k+1)^(n-k) / 2];
Table[A369072[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Jan 13 2024 *)

SageMath

def A369072(n, k):
    return binomial(n, k-1)*(k-1)^(k-1)*n*(n-k+1)^(n-k)//2
for n in range(9): print([A369072(n, k) for k in range(n+1)])