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A369072
Triangle read by rows: T(n, k) = floor(binomial(n, k - 1) * (k - 1)^(k - 1) * n * (n - k + 1)^(n - k) / 2).
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
0,5
EXAMPLE
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]
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 *)
PROG
(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)])
CROSSREFS
Cf. A057065 (column 1), A369027 (main diagonal).
Sequence in context: A244137 A354127 A181389 * A091466 A134085 A151339
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Jan 12 2024
STATUS
approved