A369025
Triangle read by rows: T(n, k) = floor(binomial(n, k - 1) * (k - 1)^(k - 1) * k *(n - k + 1)^(n - k) / 2).
Original entry on oeis.org
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
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]
-
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 *)
-
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)])
A369026
a(n) = floor(n^(n - 1) / 2) for n > 0 and otherwise 0.
Original entry on oeis.org
0, 0, 1, 4, 32, 312, 3888, 58824, 1048576, 21523360, 500000000, 12968712300, 371504185344, 11649042561240, 396857386627072, 14596463012695312, 576460752303423488, 24330595937833434240, 1092955779869348265984
Offset: 0
A369072
Triangle read by rows: T(n, k) = floor(binomial(n, k - 1) * (k - 1)^(k - 1) * n * (n - k + 1)^(n - k) / 2).
Original entry on oeis.org
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
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]
-
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 *)
-
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)])
Showing 1-3 of 3 results.