A369019 - OEIS

%I #15 Jan 27 2024 18:48:35

%S 0,0,1,0,2,4,0,9,12,36,0,64,72,144,432,0,625,640,1080,2160,6400,0,

%T 7776,7500,11520,19440,38400,112500,0,117649,108864,157500,241920,

%U 403200,787500,2286144,0,2097152,1882384,2612736,3780000,5734400,9450000,18289152,52706752

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

%F T = A369018 - A368849.

%e Triangle starts:

%e [0] [0]

%e [1] [0,      1]

%e [2] [0,      2,      4]

%e [3] [0,      9,     12,     36]

%e [4] [0,     64,     72,    144,    432]

%e [5] [0,    625,    640,   1080,   2160,   6400]

%e [6] [0,   7776,   7500,  11520,  19440,  38400, 112500]

%e [7] [0, 117649, 108864, 157500, 241920, 403200, 787500, 2286144]

%p T := (n, k) -> binomial(n, k - 1)*(k - 1)^(k - 1)*k*(n - k + 1)^(n - k):

%p seq(seq(T(n, k), k = 0..n), n=0..9);

%t A369019[n_, k_] := Binomial[n, k-1] If[k == 1, 1, (k-1)^(k-1)] k (n-k+1)^(n-k);

%t Table[A369019[n, k], {n, 0, 10}, {k, 0, n}] (* _Paolo Xausa_, Jan 27 2024 *)

%o (SageMath)

%o def A369019(n, k):

%o     return binomial(n, k - 1)*(k - 1)^(k - 1)*k*(n - k + 1)^(n - k)

%Y Cf. A369018, A368849.

%K nonn,tabl

%O 0,5

%A _Peter Luschny_, Jan 13 2024