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A162498 Triangle read by rows: T(n, k) = Sum_{j=0..k} (-1)^j*binomial(n, j)*(k + 1 - j)^(n - 1).

%I A162498 #16 Aug 16 2025 09:37:49
%S A162498 1,1,1,3,4,1,23,33,11,1,425,620,220,26,1,18129,26525,9520,1180,57,1,
%T A162498 1721419,2519664,905765,113050,5649,120,1,353654167,517670461,
%U A162498 186123259,23248085,1166221,25347,247,1,153923102577,225309742552,81009042744,10119247684,507795498,11059468,109386,502,1
%N A162498 Triangle read by rows: T(n, k) = Sum_{j=0..k} (-1)^j*binomial(n, j)*(k + 1 - j)^(n - 1).
%e A162498 Triangle begins:
%e A162498   {1},
%e A162498   {1, 1},
%e A162498   {3, 4, 1},
%e A162498   {23, 33, 11, 1},
%e A162498   {425, 620, 220, 26, 1},
%e A162498   {18129, 26525, 9520, 1180, 57, 1},
%e A162498   {1721419, 2519664, 905765, 113050, 5649, 120, 1},
%e A162498   {353654167, 517670461, 186123259, 23248085, 1166221, 25347, 247, 1},
%e A162498   {153923102577, 225309742552, 81009042744, 10119247684, 507795498, 11059468, 109386, 502, 1},
%e A162498   ...
%t A162498 t[n_,k_]:=Sum[(-1)^j Binomial[n,j](k+1-j)^(n-1),{j,0,k}];
%t A162498 M[n_]:=Table[If[k <= m,(-1)^(m+k)*t[m,k],0],{k,0,n-2},{m,2,n}];
%t A162498 Flatten[Table[Table[Inverse[M[12]][[m,n]],{m,1,n}],{n,1,11}]]
%Y A162498 Cf. A154921. An unsigned version of A055325.
%K A162498 nonn,easy,tabl
%O A162498 1,4
%A A162498 _Roger L. Bagula_ and _Mats Granvik_, Dec 06 2009