A153188 Triangle read by rows: T(n,k) = n^k * k!.

1, 1, 1, 1, 2, 8, 1, 3, 18, 162, 1, 4, 32, 384, 6144, 1, 5, 50, 750, 15000, 375000, 1, 6, 72, 1296, 31104, 933120, 33592320, 1, 7, 98, 2058, 57624, 2016840, 84707280, 4150656720, 1, 8, 128, 3072, 98304, 3932160, 188743680, 10569646080, 676457349120

Offset: 0

Author

Roger L. Bagula, Dec 20 2008

Keywords

• nonn
• tabl

Examples

			Triangle T(n,k) begins:
  1;
  1, 1;
  1, 2,  8;
  1, 3, 18,  162;
  1, 4, 32,  384,  6144;
  1, 5, 50,  750, 15000,  375000;
  1, 6, 72, 1296, 31104,  933120, 33592320;
  1, 7, 98, 2058, 57624, 2016840, 84707280, 4150656720;
  ...
		

Crossrefs

Main diagonal gives A061711.

Row sums give A368561.

Cf. A000165, A008544.

Programs

Mathematica

t[n_, m_] =Product[m*k, {k, 1, n}];
Table[Table[t[n, m], {n, 1, m}], {m, 1, 10}];
Flatten[%]

Formula

T(n,k) = Product_{j=1..n} n*j.

Extensions

Formula corrected by Georg Fischer, Oct 24 2024