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

%I A177428 #5 May 15 2016 23:36:46
%S A177428 1,1,1,1,8,2,1,33,66,6,1,104,792,624,24,1,285,6040,18120,6840,120,1,
%T A177428 720,35730,289920,428760,86400,720,1,1729,180306,3279990,13119960,
%U A177428 10818360,1244880,5040,1,4016,818048,29646624,262399200,592932480,294497280
%N A177428 Triangle T(n,m)= A141686(n,m)*(m-1)! read by rows, n>=1, 1<=m<=n.
%C A177428 Row sums are 1, 2, 11, 106, 1545, 31406, 842251, 28650266, 1200578609, 60585995422,
%C A177428 3615590440731,....
%F A177428 T(n,m)= A008292(n,m)*(n-1)!/(n-m)!.
%e A177428 1;
%e A177428 1, 1;
%e A177428 1, 8, 2;
%e A177428 1, 33, 66, 6;
%e A177428 1, 104, 792, 624, 24;
%e A177428 1, 285, 6040, 18120, 6840, 120;
%e A177428 1, 720, 35730, 289920, 428760, 86400, 720;
%e A177428 1, 1729, 180306, 3279990, 13119960, 10818360, 1244880, 5040;
%p A177428 A177428 := proc(n,k)
%p A177428     A008292(n,k)*(n-1)!/(n-k)! ;
%p A177428 end proc: # _R. J. Mathar_, May 15 2016
%t A177428 << DiscreteMath`Combinatorica`
%t A177428 t[n_, m_] = Eulerian[n + 1, m]*n!/(n - m)!;
%t A177428 Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t A177428 Flatten[%]
%K A177428 nonn,tabl
%O A177428 1,5
%A A177428 _Roger L. Bagula_, May 08 2010
%E A177428 Edited by _R. J. Mathar_, May 15 2016