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A369025
Triangle read by rows: T(n, k) = floor(binomial(n, k - 1) * (k - 1)^(k - 1) * k *(n - k + 1)^(n - k) / 2).
4
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
0,6
EXAMPLE
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]
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 *)
PROG
(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)])
CROSSREFS
Cf. A369026 (column 1), A369027 (main diagonal).
Sequence in context: A287846 A085623 A317965 * A190791 A002885 A344769
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Jan 12 2024
STATUS
approved