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%I A271701 #7 Apr 18 2016 06:38:29
%S A271701 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 A271701 1782,0,1,7,34,153,681,3068,14121,0,1,8,43,211,1016,4929,24361,123244,
%U A271701 0,1,9,53,281,1451,7515,39537,212509,1169832
%N A271701 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 A271701 Triangle starts:
%e A271701 [1]
%e A271701 [0, 1]
%e A271701 [0, 1, 2]
%e A271701 [0, 1, 3, 8]
%e A271701 [0, 1, 4, 13, 41]
%e A271701 [0, 1, 5, 19, 69,  252]
%e A271701 [0, 1, 6, 26, 106, 431, 1782]
%e A271701 [0, 1, 7, 34, 153, 681, 3068, 14121]
%p A271701 T := (n,k) -> add(Stirling2(k,j)*binomial(-j,-n)*(-1)^(n-j),j=0..n);
%p A271701 seq(seq(T(n,k), k=0..n), n=0..9);
%t A271701 Flatten[Table[Sum[(-1)^(n-j) Binomial[-j,-n] StirlingS2[k,j], {j,0,n}], {n,0,9},{k,0,n}]]
%K A271701 nonn,tabl
%O A271701 0,6
%A A271701 _Peter Luschny_, Apr 14 2016

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