%I #7 Jul 31 2015 01:24:07
%S 1,1,1,1,2,3,2,6,12,4,6,24,60,20,10,24,120,360,120,60,36,120,720,2520,
%T 840,420,252,168,720,5040,20160,6720,3360,2016,1344,960,5040,40320,
%U 181440,60480,30240,18144,12096,8640,6480,40320,362880,1814400,604800
%N Triangle read by rows: see below.
%e Consider the formula n! = 1*2*3...*(n-2) + 2*3*4...*(n-1)+ ...+ (n-1)*n*1*2...(n-4) + n*1*2*3*...*(n-3). E.g., 5! = 1*2*3 +2*3*4 +3*4*5 + 4*5*1 + 5*1*2.
%e Consider the following triangle of partition of n! based on above formula.
%e 1
%e 1 1
%e 1 2 3
%e 2 6 12 4
%e 6 24 60 20 10
%e 24 120 360 120 60 36
%e ...
%e Sequence contains the triangle by rows.
%t f[n_] := Times @@@ Sort[Partition[Range[n], n - 2, 1, {-1, -1}]]; Flatten[ Table[ f[n], {n, 2, 10}]] (* _Robert G. Wilson v_, Jul 13 2005 *)
%K nonn,tabl
%O 1,5
%A _Amarnath Murthy_, Jul 10 2005
%E More terms from _Robert G. Wilson v_, Jul 18 2005