%I #24 Oct 09 2017 00:02:02

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

%T -1,-2,0,5,-5,1,0,1,-1,-2,0,1,1,9,-1,0,1,-1,-2,0,1,9,-12,3,2,0,1,-1,

%U -2,0,1,4,-4,-3,-20,-2,0,1,-1,-2,0,1,4,6,-15,31,16,2

%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/(1 + Sum_{j=1..k} j*x^(j*i)).

%H Seiichi Manyama, <a href="/A290217/b290217.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, 0, 0, ...

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

%e 0, -1, -5, 1, 9, ...

%Y Columns k=0..3 give A000007, A081362, A293287, A290395.

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

%Y Main diagonal gives A258210.

%Y Cf. A290216, A293307.

%K sign,tabl

%O 0,13

%A _Seiichi Manyama_, Oct 06 2017