login
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} (-1)^j*j*x^(j*i)).
5

%I #22 Jan 06 2018 18:45:15

%S 1,1,0,1,1,0,1,1,2,0,1,1,0,3,0,1,1,0,-1,5,0,1,1,0,2,-1,7,0,1,1,0,2,5,

%T 3,11,0,1,1,0,2,1,3,3,15,0,1,1,0,2,1,-5,0,-1,22,0,1,1,0,2,1,0,0,11,-8,

%U 30,0,1,1,0,2,1,0,10,7,25,-8,42,0,1,1,0,2,1,0

%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} (-1)^j*j*x^(j*i)).

%H Seiichi Manyama, <a href="/A293307/b293307.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, 2, 0, 0, 0, ...

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

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

%e 0, 7, 3, 3, -5, ...

%Y Columns k=0..2 give A000007, A000041, A293294.

%Y Rows n=0..1 give A000012, A057427.

%Y Main diagonal gives A122792.

%Y Cf. A293293, A293305.

%K sign,tabl

%O 0,9

%A _Seiichi Manyama_, Oct 05 2017