cp's OEIS Frontend

A369017 Triangle read by rows: T(n, k) = binomial(n-1, k-1) * (k - 1)^(k - 1) * k * (n - k + 1)^(n - k - 1).

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