A076482 Triangle with T(n,k)=n!*(k-1)^k/k! where 1<=k<=n.

0, 0, 1, 0, 3, 8, 0, 12, 32, 81, 0, 60, 160, 405, 1024, 0, 360, 960, 2430, 6144, 15625, 0, 2520, 6720, 17010, 43008, 109375, 279936, 0, 20160, 53760, 136080, 344064, 875000, 2239488, 5764801, 0, 181440, 483840, 1224720, 3096576, 7875000, 20155392, 51883209, 134217728

Offset: 1

Author

Henry Bottomley, Oct 14 2002

Keywords

• nonn
• tabl

Examples

			Rows start
  0;
  0,   1;
  0,   3,   8;
  0,  12,  32,   81;
  0,  60, 160,  405, 1024;
  0, 360, 960, 2430, 6144, 15625;
  ...
		

Links

• Seiichi Manyama, Rows n = 1..140, flattened

Crossrefs

Row sums are A076483.

Cf. A001710, A007778, A008279.

Programs

Mathematica

Table[n! (k-1)^k/k!,{n,0,10},{k,n}]//Flatten (* Harvey P. Dale, Nov 28 2019 *)

Formula

T(n,k) = n*T(n, k-1) = A007778(k-1)*A008279(n,n-k) starting with T(n,n) = (n-1)^n = A007778(n-1).