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Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} 1/(Sum_{j=0..k} j!*x^(j*i)).
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%I #20 Oct 06 2017 21:33:21

%S 1,1,0,1,-1,0,1,-1,0,0,1,-1,-2,-1,0,1,-1,-2,3,1,0,1,-1,-2,-3,-1,-1,0,

%T 1,-1,-2,-3,11,-5,1,0,1,-1,-2,-3,-13,7,9,-1,0,1,-1,-2,-3,-13,55,-15,3,

%U 2,0,1,-1,-2,-3,-13,-65,33,-63,-20,-2,0,1,-1,-2,-3,-13,-65

%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} 1/(Sum_{j=0..k} j!*x^(j*i)).

%H Seiichi Manyama, <a href="/A293285/b293285.txt">Antidiagonals n = 0..139, flattened</a>

%e Square array begins:

%e 1, 1, 1, 1, 1, ...

%e 0, -1, -1, -1, -1, ...

%e 0, 0, -2, -2, -2, ...

%e 0, -1, 3, -3, -3, ...

%e 0, 1, -1, 11, -13, ...

%e 0, -1, -5, 7, 55, ...

%Y Columns k=0..2 give A000007, A081362, A293287.

%Y Rows n=0..1 give A000012, (-1)*A057427.

%Y Main diagonal gives A293251.

%Y Cf. A293202, A293293.

%K sign,tabl,look

%O 0,13

%A _Seiichi Manyama_, Oct 04 2017