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A369017
Triangle read by rows: T(n, k) = binomial(n-1, k-1) * (k - 1)^(k - 1) * k * (n - k + 1)^(n - k - 1).
2
0, 0, 1, 0, 1, 2, 0, 3, 4, 12, 0, 16, 18, 36, 108, 0, 125, 128, 216, 432, 1280, 0, 1296, 1250, 1920, 3240, 6400, 18750, 0, 16807, 15552, 22500, 34560, 57600, 112500, 326592, 0, 262144, 235298, 326592, 472500, 716800, 1181250, 2286144, 6588344
OFFSET
0,6
FORMULA
T = B066320 - A369016 (where B066320 = A066320 after adding a 0-column to the left and then setting offset to (0, 0)).
EXAMPLE
Triangle starts:
[0][0]
[1][0, 1]
[2][0, 1, 2]
[3][0, 3, 4, 12]
[4][0, 16, 18, 36, 108]
[5][0, 125, 128, 216, 432, 1280]
[6][0, 1296, 1250, 1920, 3240, 6400, 18750]
[7][0, 16807, 15552, 22500, 34560, 57600, 112500, 326592]
[8][0, 262144, 235298, 326592, 472500, 716800, 1181250, 2286144, 6588344]
MAPLE
T := (n, k) -> binomial(n-1, k-1)*(k-1)^(k-1)*k*(n-k+1)^(n-k-1):
seq(seq(T(n, k), k = 0..n), n=0..9);
MATHEMATICA
A369017[n_, k_] := Binomial[n-1, k-1] If[k == 1, 1, (k-1)^(k-1)] k (n-k+1)^(n-k-1);
Table[A369017[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Jan 28 2024 *)
PROG
(Julia)
T(n, k) = binomial(n-1, k-1)*(k-1)^(k-1)*k*(n-k+1)^(n-k-1)
for n in 0:9 (println([T(n, k) for k in 0:n])) end
(PARI) T(n, k) = binomial(n-1, k-1) * (k - 1)^(k - 1) * k * (n - k + 1)^(n - k - 1) \\ Winston de Greef, Jan 27 2024
CROSSREFS
Sequence in context: A254213 A321171 A336973 * A352846 A035347 A094126
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Jan 12 2024
STATUS
approved