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%I #11 Sep 30 2017 04:39:51
%S 1,1,-1,1,-1,0,1,0,-1,1,1,0,-1,2,1,1,0,0,-3,9,-2,1,0,0,-1,-3,4,-9,1,0,
%T 0,0,-4,20,-95,-9,1,0,0,0,-1,-10,150,-414,50,1,0,0,0,0,-5,-10,504,49,
%U 267,1,0,0,0,0,-1,-15,105,-343,10088,413,1,0,0,0,0,0,-6
%N Square array A(n,k), n>=0, k>=0, read by antidiagonals, where A(0,k) = 1 and A(n,k) = - Sum_{i=0..n-1} binomial(n-1,i) * binomial(i+1,k) * A(n-1-i,k) for n > 0.
%H Seiichi Manyama, <a href="/A293015/b293015.txt">Antidiagonals n = 0..139, flattened</a>
%e Square array begins:
%e 1, 1, 1, 1, 1, ...
%e -1, -1, 0, 0, 0, ...
%e 0, -1, -1, 0, 0, ...
%e 1, 2, -3, -1, 0, ...
%e 1, 9, -3, -4, -1, ...
%Y Columns k=0-4 give: A000587, A292952, A292953, A292954, A292955.
%Y Rows n=0 gives A000012.
%Y Cf. A145460.
%K sign,tabl
%O 0,14
%A _Seiichi Manyama_, Sep 28 2017