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%I #17 Oct 08 2017 17:38:49
%S 1,1,0,1,2,0,1,2,3,0,1,2,7,6,0,1,2,7,10,9,0,1,2,7,16,25,14,0,1,2,7,16,
%T 31,38,22,0,1,2,7,16,39,62,78,32,0,1,2,7,16,39,70,117,116,46,0,1,2,7,
%U 16,39,80,149,206,206,66,0,1,2,7,16,39,80,159,262,362
%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=1..k} j*x^(j*i))^2.
%H Seiichi Manyama, <a href="/A293377/b293377.txt">Antidiagonals n = 0..139, flattened</a>
%e Square array begins:
%e 1, 1, 1, 1, 1, ...
%e 0, 2, 2, 2, 2, ...
%e 0, 3, 7, 7, 7, ...
%e 0, 6, 10, 16, 16, ...
%e 0, 9, 25, 31, 39, ...
%e 0, 14, 38, 62, 70, ...
%Y Columns k=0..1 give A000007, A022567.
%Y Rows n=0 gives A000012.
%Y Main diagonal gives A293378.
%Y Product_{i>0} (1 + Sum_{j=1..k} j*x^(j*i))^m: A290217 (m=-1), A290216 (m=1), this sequence (m=2).
%K nonn,tabl
%O 0,5
%A _Seiichi Manyama_, Oct 07 2017