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%I #5 Mar 30 2012 17:34:32
%S 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,-4,-4,1,1,1,1,-22,-24,-22,1,1,1,1,
%T -118,-114,-114,-118,1,1,1,1,-718,-594,-528,-594,-718,1,1,1,1,-5038,
%U -3594,-2736,-2736,-3594,-5038,1,1,1,1,-40318,-25194,-16536,-14160
%N Triangle read by rows: t(n,k)= k! + (1-k!)*(n - k)!, 0<=k<=n.
%C Row sums are 1, 2, 3, 4, 4, -4, -64, -460, -3148, -22732, -178252,...
%e 1;
%e 1, 1;
%e 1, 1, 1;
%e 1, 1, 1, 1;
%e 1, 1, 0, 1, 1;
%e 1, 1, -4, -4, 1, 1;
%e 1, 1, -22, -24, -22, 1, 1;
%e 1, 1, -118, -114, -114, -118, 1, 1;
%e 1, 1, -718, -594, -528, -594, -718, 1, 1;
%e 1, 1, -5038, -3594, -2736, -2736, -3594, -5038, 1, 1;
%e 1, 1, -40318, -25194, -16536, -14160, -16536, -25194, -40318, 1, 1;
%t Table[Table[(k! + (-k + n)! - k!*(n - k)!), {k, 0, n}], {n, 0, 10}];
%t Flatten[%]
%K sign,tabl
%O 0,18
%A _Roger L. Bagula_, Jan 22 2009
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