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

%I #5 May 15 2016 23:36:46

%S 1,1,1,1,8,2,1,33,66,6,1,104,792,624,24,1,285,6040,18120,6840,120,1,

%T 720,35730,289920,428760,86400,720,1,1729,180306,3279990,13119960,

%U 10818360,1244880,5040,1,4016,818048,29646624,262399200,592932480,294497280

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

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

%C 3615590440731,....

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

%e 1;

%e 1, 1;

%e 1, 8, 2;

%e 1, 33, 66, 6;

%e 1, 104, 792, 624, 24;

%e 1, 285, 6040, 18120, 6840, 120;

%e 1, 720, 35730, 289920, 428760, 86400, 720;

%e 1, 1729, 180306, 3279990, 13119960, 10818360, 1244880, 5040;

%p A177428 := proc(n,k)

%p A008292(n,k)*(n-1)!/(n-k)! ;

%p end proc: # _R. J. Mathar_, May 15 2016

%t << DiscreteMath`Combinatorica`

%t t[n_, m_] = Eulerian[n + 1, m]*n!/(n - m)!;

%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%K nonn,tabl

%O 1,5

%A _Roger L. Bagula_, May 08 2010

%E Edited by _R. J. Mathar_, May 15 2016