A293377 - OEIS

%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