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A369018 Triangle read by rows: T(n, k) = binomial(n, k - 1)*(k - 1)^(k - 1)*n*(n - k + 1)^(n - k).

%I A369018 #13 Jan 27 2024 18:48:10
%S A369018 0,0,1,0,4,4,0,27,18,36,0,256,144,192,432,0,3125,1600,1800,2700,6400,
%T A369018 0,46656,22500,23040,29160,46080,112500,0,823543,381024,367500,423360,
%U A369018 564480,918750,2286144,0,16777216,7529536,6967296,7560000,9175040,12600000,20901888,52706752
%N A369018 Triangle read by rows: T(n, k) = binomial(n, k - 1)*(k - 1)^(k - 1)*n*(n - k + 1)^(n - k).
%F A369018 T = A368849 + A369019.
%e A369018 Triangle read by rows:
%e A369018 [0] [0]
%e A369018 [1] [0,      1]
%e A369018 [2] [0,      4,      4]
%e A369018 [3] [0,     27,     18,     36]
%e A369018 [4] [0,    256,    144,    192,    432]
%e A369018 [5] [0,   3125,   1600,   1800,   2700,   6400]
%e A369018 [6] [0,  46656,  22500,  23040,  29160,  46080, 112500]
%e A369018 [7] [0, 823543, 381024, 367500, 423360, 564480, 918750, 2286144]
%p A369018 T := (n, k) -> binomial(n, k - 1)*(k - 1)^(k - 1)*n*(n - k + 1)^(n - k):
%p A369018 seq(seq(T(n, k), k = 0..n), n=0..9);
%t A369018 A369018[n_, k_] := Binomial[n, k-1] If[k == 1, 1, (k-1)^(k-1)] n (n-k+1)^(n-k);
%t A369018 Table[A369018[n, k], {n, 0, 10}, {k, 0, n}] (* _Paolo Xausa_, Jan 27 2024 *)
%o A369018 (SageMath)
%o A369018 def A369018(n, k):
%o A369018     return binomial(n, k - 1)*(k - 1)^(k - 1)*n*(n - k + 1)^(n - k)
%Y A369018 Cf. A369019, A368849.
%K A369018 nonn,tabl
%O A369018 0,5
%A A369018 _Peter Luschny_, Jan 13 2024