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A293377 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.

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