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A369017
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Triangle read by rows: T(n, k) = binomial(n-1, k-1) * (k - 1)^(k - 1) * k * (n - k + 1)^(n - k - 1).
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2
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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
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OFFSET
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0,6
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LINKS
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FORMULA
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T = B066320 - A369016 (where B066320 = A066320 after adding a 0-column to the left and then setting offset to (0, 0)).
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EXAMPLE
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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]
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MAPLE
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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);
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MATHEMATICA
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A369017[n_, k_] := Binomial[n-1, k-1] If[k == 1, 1, (k-1)^(k-1)] k (n-k+1)^(n-k-1);
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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