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%I #6 Apr 10 2013 15:35:44
%S 1,1,1,1,8,1,1,25,25,1,1,69,152,69,1,1,209,716,716,209,1,1,839,3076,
%T 5540,3076,839,1,1,4813,13504,36248,36248,13504,4813,1,1,36283,68814,
%U 216662,352652,216662,68814,36283,1,1,324585,453518,1272538,2983444
%N Triangle read by rows: let t1(n,k)=Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]; then T(n,m)=2*t1(n + 1, k) - (m! - n! + (-m + n)!).
%C Row sums are {1, 2, 10, 52, 292, 1852, 13372, 109132, 996172, 10068172, 111674572,...}.
%e {1},
%e {1, 1},
%e {1, 8, 1},
%e {1, 25, 25, 1},
%e {1, 69, 152, 69, 1},
%e {1, 209, 716, 716, 209, 1},
%e {1, 839, 3076, 5540, 3076, 839, 1},
%e {1, 4813, 13504, 36248, 36248, 13504, 4813, 1},
%e {1, 36283, 68814, 216662, 352652, 216662, 68814, 36283, 1},
%e {1, 324585, 453518, 1272538, 2983444, 2983444, 1272538, 453518, 324585, 1},
%e {1, 3269991, 3893752, 8030730, 23104284, 35077056, 23104284, 8030730, 3893752, 3269991, 1}
%t t[n_, k_] = Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}];
%t Table[Table[(2*t[n + 1, k] - (k! - n! + (-k + n)!)), {k, 0, n}], {n, 0, 10}];
%t Flatten[%]
%K nonn,tabl
%O 0,5
%A _Roger L. Bagula_, Jan 22 2009
%E Edited by _N. J. A. Sloane_, Jan 25 2009
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