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A369072 Triangle read by rows: T(n, k) = floor(binomial(n, k - 1) * (k - 1)^(k - 1) * n * (n - k + 1)^(n - k) / 2).

%I A369072 #8 Jan 13 2024 15:05:46
%S A369072 0,0,0,0,2,2,0,13,9,18,0,128,72,96,216,0,1562,800,900,1350,3200,0,
%T A369072 23328,11250,11520,14580,23040,56250,0,411771,190512,183750,211680,
%U A369072 282240,459375,1143072,0,8388608,3764768,3483648,3780000,4587520,6300000,10450944,26353376
%N A369072 Triangle read by rows: T(n, k) = floor(binomial(n, k - 1) * (k - 1)^(k - 1) * n * (n - k + 1)^(n - k) / 2).
%e A369072 Triangle starts:
%e A369072 [0] [0]
%e A369072 [1] [0,      0]
%e A369072 [2] [0,      2,      2]
%e A369072 [3] [0,     13,      9,     18]
%e A369072 [4] [0,    128,     72,     96,    216]
%e A369072 [5] [0,   1562,    800,    900,   1350,   3200]
%e A369072 [6] [0,  23328,  11250,  11520,  14580,  23040,  56250]
%e A369072 [7] [0, 411771, 190512, 183750, 211680, 282240, 459375, 1143072]
%t A369072 A369072[n_, k_] := Floor[Binomial[n, k-1] If[k == 1, 1, (k-1)^(k-1)] n (n-k+1)^(n-k) / 2];
%t A369072 Table[A369072[n, k], {n, 0, 10}, {k, 0, n}] (* _Paolo Xausa_, Jan 13 2024 *)
%o A369072 (SageMath)
%o A369072 def A369072(n, k):
%o A369072     return binomial(n, k-1)*(k-1)^(k-1)*n*(n-k+1)^(n-k)//2
%o A369072 for n in range(9): print([A369072(n, k) for k in range(n+1)])
%Y A369072 Cf. A057065 (column 1), A369027 (main diagonal).
%K A369072 nonn,tabl
%O A369072 0,5
%A A369072 _Peter Luschny_, Jan 12 2024