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%I #7 Feb 10 2013 10:34:17
%S 1,1,1,3,4,1,23,33,11,1,425,620,220,26,1,18129,26525,9520,1180,57,1,
%T 1721419,2519664,905765,113050,5649,120,1,353654167,517670461,
%U 186123259,23248085,1166221,25347,247,1,153923102577,225309742552,81009042744
%N Triangle read by rows: T(n,k) = Sum[(-1)^j Binomial[n, j](k + 1 - j)^(n - 1), {j, 0, k}].
%C Row sums are: {1, 2, 8, 68, 1292, 55412, 5265668, 1081887788, 470880100412, 427569972956852, 800992247015505668,...}.
%e {1},
%e {1, 1},
%e {3, 4, 1},
%e {23, 33, 11, 1},
%e {425, 620, 220, 26, 1},
%e {18129, 26525, 9520, 1180, 57, 1},
%e {1721419, 2519664, 905765, 113050, 5649, 120, 1},
%e {353654167, 517670461, 186123259, 23248085, 1166221, 25347, 247, 1},
%e {153923102577, 225309742552, 81009042744, 10119247684, 507795498, 11059468, 109386, 502, 1},
%e {139765654884545, 204586385695065, 73558129319520, 9188556369384, 461102826618, 10043953290, 99446730, 460686, 1013, 1},
%e {261831303051976691, 383263833094891100, 137800821538668585, 17213473445481060, 863812603482906, 18816103842228, 186311714820, 863536410, 1909831, 2036, 1} (End)
%t t[n_,k_]:=Sum[(-1)^j Binomial[n,j](k+1-j)^(n-1),{j,0,k}];
%t M[n_]:=Table[If[k <= m,(-1)^(m+k)*t[m,k],0],{k,0,n-2},{m,2,n}]; Flatten[Table[Table[Inverse[M[12]][[m,n]],{m,1,n}],{n,1,11}]]
%Y Cf. A154921. An unsigned version of A055325.
%K nonn,easy,tabl
%O 1,4
%A _Roger L. Bagula_ and Mats Granvik, Dec 06 2009
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