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%I #20 Jan 28 2024 18:06:35
%S 0,0,1,0,1,2,0,3,4,12,0,16,18,36,108,0,125,128,216,432,1280,0,1296,
%T 1250,1920,3240,6400,18750,0,16807,15552,22500,34560,57600,112500,
%U 326592,0,262144,235298,326592,472500,716800,1181250,2286144,6588344
%N Triangle read by rows: T(n, k) = binomial(n-1, k-1) * (k - 1)^(k - 1) * k * (n - k + 1)^(n - k - 1).
%H Winston de Greef, <a href="/A369017/b369017.txt">Table of n, a(n) for the first 150 rows, flattened (n = 0..11324)</a>
%F T = B066320 - A369016 (where B066320 = A066320 after adding a 0-column to the left and then setting offset to (0, 0)).
%e Triangle starts:
%e [0][0]
%e [1][0, 1]
%e [2][0, 1, 2]
%e [3][0, 3, 4, 12]
%e [4][0, 16, 18, 36, 108]
%e [5][0, 125, 128, 216, 432, 1280]
%e [6][0, 1296, 1250, 1920, 3240, 6400, 18750]
%e [7][0, 16807, 15552, 22500, 34560, 57600, 112500, 326592]
%e [8][0, 262144, 235298, 326592, 472500, 716800, 1181250, 2286144, 6588344]
%p T := (n, k) -> binomial(n-1, k-1)*(k-1)^(k-1)*k*(n-k+1)^(n-k-1):
%p seq(seq(T(n, k), k = 0..n), n=0..9);
%t A369017[n_, k_] := Binomial[n-1, k-1] If[k == 1, 1, (k-1)^(k-1)] k (n-k+1)^(n-k-1);
%t Table[A369017[n, k], {n, 0, 10}, {k, 0, n}] (* _Paolo Xausa_, Jan 28 2024 *)
%o (Julia)
%o T(n, k) = binomial(n-1, k-1)*(k-1)^(k-1)*k*(n-k+1)^(n-k-1)
%o for n in 0:9 (println([T(n, k) for k in 0:n])) end
%o (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
%Y Cf. A066320, A369016.
%K nonn,tabl
%O 0,6
%A _Peter Luschny_, Jan 12 2024
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