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%I #5 Apr 10 2013 15:42:44
%S 1,1,1,2,2,2,6,6,6,6,24,24,25,24,24,120,120,125,125,120,120,720,720,
%T 743,745,743,720,720,5040,5040,5159,5155,5155,5159,5040,5040,40320,
%U 40320,41039,40915,40849,40915,41039,40320,40320,362880,362880,367919,366475
%N Triangle read by rows: t(n,m)=1 - (k! - n! + (-k + n)! - k!*(n - k)!).
%C Row sums are:
%C {1, 2, 6, 24, 121, 730, 5111, 40788, 366037, 3651542, 40095063,...}.
%F t(n,m)=t(n,m)=1 - (k! - n! + (-k + n)! - k!*(n - k)!)..
%e {1},
%e {1, 1},
%e {2, 2, 2},
%e {6, 6, 6, 6},
%e {24, 24, 25, 24, 24},
%e {120, 120, 125, 125, 120, 120},
%e {720, 720, 743, 745, 743, 720, 720},
%e {5040, 5040, 5159, 5155, 5155, 5159, 5040, 5040},
%e {40320, 40320, 41039, 40915, 40849, 40915, 41039, 40320, 40320},
%e {362880, 362880, 367919, 366475, 365617, 365617, 366475, 367919, 362880, 362880},
%e {3628800, 3628800, 3669119, 3653995, 3645337, 3642961, 3645337, 3653995, 3669119, 3628800, 3628800}
%t Table[Table[1 - (k! - n! + (-k + n)! - k!*(n - k)!), {k, 0, n}], {n, 0, 10}];
%t Flatten[%]
%K nonn,uned,tabl
%O 0,4
%A _Roger L. Bagula_, Jan 22 2009
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