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

0, 0, 1, 0, 1, 2, 0, 3, 4, 12, 0, 16, 18, 36, 108, 0, 125, 128, 216, 432, 1280, 0, 1296, 1250, 1920, 3240, 6400, 18750, 0, 16807, 15552, 22500, 34560, 57600, 112500, 326592, 0, 262144, 235298, 326592, 472500, 716800, 1181250, 2286144, 6588344

Offset: 0

Author

Peter Luschny, Jan 12 2024

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0][0]
[1][0,      1]
[2][0,      1,      2]
[3][0,      3,      4,     12]
[4][0,     16,     18,     36,    108]
[5][0,    125,    128,    216,    432,   1280]
[6][0,   1296,   1250,   1920,   3240,   6400,   18750]
[7][0,  16807,  15552,  22500,  34560,  57600,  112500,  326592]
[8][0, 262144, 235298, 326592, 472500, 716800, 1181250, 2286144, 6588344]
		

Links

• Winston de Greef, Table of n, a(n) for the first 150 rows, flattened (n = 0..11324)

Crossrefs

Cf. A066320, A369016.

Programs

Julia

T(n, k) = binomial(n-1, k-1)*(k-1)^(k-1)*k*(n-k+1)^(n-k-1)
for n in 0:9 (println([T(n, k) for k in 0:n])) end

Maple

T := (n, k) -> binomial(n-1, k-1)*(k-1)^(k-1)*k*(n-k+1)^(n-k-1):
seq(seq(T(n, k), k = 0..n), n=0..9);

Mathematica

A369017[n_, k_] := Binomial[n-1, k-1] If[k == 1, 1, (k-1)^(k-1)] k (n-k+1)^(n-k-1);
Table[A369017[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Jan 28 2024 *)

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

Formula

T = B066320 - A369016 (where B066320 = A066320 after adding a 0-column to the left and then setting offset to (0, 0)).