%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