A177428 Triangle T(n,m)= A141686(n,m)*(m-1)! read by rows, n>=1, 1<=m<=n.

1, 1, 1, 1, 8, 2, 1, 33, 66, 6, 1, 104, 792, 624, 24, 1, 285, 6040, 18120, 6840, 120, 1, 720, 35730, 289920, 428760, 86400, 720, 1, 1729, 180306, 3279990, 13119960, 10818360, 1244880, 5040, 1, 4016, 818048, 29646624, 262399200, 592932480, 294497280

Offset: 1

Author

Roger L. Bagula, May 08 2010

Keywords

• nonn
• tabl

Comments

Row sums are 1, 2, 11, 106, 1545, 31406, 842251, 28650266, 1200578609, 60585995422,

3615590440731,....

Examples

			1;
1, 1;
1, 8, 2;
1, 33, 66, 6;
1, 104, 792, 624, 24;
1, 285, 6040, 18120, 6840, 120;
1, 720, 35730, 289920, 428760, 86400, 720;
1, 1729, 180306, 3279990, 13119960, 10818360, 1244880, 5040;
		

Programs

Maple

A177428 := proc(n,k)
    A008292(n,k)*(n-1)!/(n-k)! ;
end proc: # R. J. Mathar, May 15 2016

Mathematica

<< DiscreteMath`Combinatorica`
t[n_, m_] = Eulerian[n + 1, m]*n!/(n - m)!;
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Formula

T(n,m)= A008292(n,m)*(n-1)!/(n-m)!.

Extensions

Edited by R. J. Mathar, May 15 2016