%I #7 Apr 18 2016 06:38:29

%S 1,0,1,0,1,2,0,1,3,8,0,1,4,13,41,0,1,5,19,69,252,0,1,6,26,106,431,

%T 1782,0,1,7,34,153,681,3068,14121,0,1,8,43,211,1016,4929,24361,123244,

%U 0,1,9,53,281,1451,7515,39537,212509,1169832

%N Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j,-n)*S2(k,j), S2 the Stirling set numbers A048993, for n>=0 and 0<=k<=n.

%e Triangle starts:

%e [1]

%e [0, 1]

%e [0, 1, 2]

%e [0, 1, 3, 8]

%e [0, 1, 4, 13, 41]

%e [0, 1, 5, 19, 69, 252]

%e [0, 1, 6, 26, 106, 431, 1782]

%e [0, 1, 7, 34, 153, 681, 3068, 14121]

%p T := (n,k) -> add(Stirling2(k,j)*binomial(-j,-n)*(-1)^(n-j),j=0..n);

%p seq(seq(T(n,k), k=0..n), n=0..9);

%t Flatten[Table[Sum[(-1)^(n-j) Binomial[-j,-n] StirlingS2[k,j], {j,0,n}], {n,0,9},{k,0,n}]]

%K nonn,tabl

%O 0,6

%A _Peter Luschny_, Apr 14 2016