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Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1 + k*x^j).
2

%I #16 Sep 09 2017 12:15:15

%S 1,1,0,1,-1,0,1,-2,0,0,1,-3,2,-1,0,1,-4,6,-6,1,0,1,-5,12,-21,14,-1,0,

%T 1,-6,20,-52,69,-26,1,0,1,-7,30,-105,220,-201,50,-1,0,1,-8,42,-186,

%U 545,-868,591,-102,2,0,1,-9,56,-301,1146,-2705,3436,-1785,214,-2,0

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

%H Seiichi Manyama, <a href="/A292133/b292133.txt">Antidiagonals n = 0..139, flattened</a>

%e Square array begins:

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

%e 0, -1, -2, -3, -4, ...

%e 0, 0, 2, 6, 12, ...

%e 0, -1, -6, -21, -52, ...

%e 0, 1, 14, 69, 220, ...

%Y Columns k=0..3 give A000007, A081362, A071109, A261582.

%Y Rows n=0..1 give A000012, (-1)*A001477.

%Y Main diagonal gives A292134.

%Y Cf. A246935, A286957.

%K sign,tabl

%O 0,8

%A _Seiichi Manyama_, Sep 09 2017