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A369025 Triangle read by rows: T(n, k) = floor(binomial(n, k - 1) * (k - 1)^(k - 1) * k *(n - k + 1)^(n - k) / 2).

%I A369025 #17 Jan 13 2024 15:09:56
%S A369025 0,0,0,0,1,2,0,4,6,18,0,32,36,72,216,0,312,320,540,1080,3200,0,3888,
%T A369025 3750,5760,9720,19200,56250,0,58824,54432,78750,120960,201600,393750,
%U A369025 1143072,0,1048576,941192,1306368,1890000,2867200,4725000,9144576,26353376
%N A369025 Triangle read by rows: T(n, k) = floor(binomial(n, k - 1) * (k - 1)^(k - 1) * k *(n - k + 1)^(n - k) / 2).
%e A369025 Triangle starts:
%e A369025   [0] [0]
%e A369025   [1] [0,     0]
%e A369025   [2] [0,     1,     2]
%e A369025   [3] [0,     4,     6,    18]
%e A369025   [4] [0,    32,    36,    72,    216]
%e A369025   [5] [0,   312,   320,   540,   1080,   3200]
%e A369025   [6] [0,  3888,  3750,  5760,   9720,  19200,  56250]
%e A369025   [7] [0, 58824, 54432, 78750, 120960, 201600, 393750, 1143072]
%t A369025 A369025[n_, k_] := Floor[Binomial[n, k-1] If[k == 1, 1, (k-1)^(k-1)] k (n-k+1)^(n-k) / 2];
%t A369025 Table[A369025[n, k], {n, 0, 10}, {k, 0, n}] (* _Paolo Xausa_, Jan 12 2024 *)
%o A369025 (SageMath)
%o A369025 def A369025(n, k):
%o A369025     return binomial(n, k-1)*(k-1)^(k-1)*k*(n-k+1)^(n-k)//2
%o A369025 for n in range(9): print([A369025(n, k) for k in range(n+1)])
%Y A369025 Cf. A369026 (column 1), A369027 (main diagonal).
%K A369025 nonn,tabl
%O A369025 0,6
%A A369025 _Peter Luschny_, Jan 12 2024