%I #19 Nov 08 2017 12:02:41

%S 1,1,-1,1,-1,-1,1,-1,-16,0,1,-1,-256,-713,0,1,-1,-4096,-531185,-64711,

%T 1,1,-1,-65536,-387416393,-4294405135,-9688521,0,1,-1,-1048576,

%U -282429470945,-281474581032631,-95363000655153,-2165724176,1,1

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

%H Seiichi Manyama, <a href="/A294699/b294699.txt">Antidiagonals n = 0..38, flattened</a>

%F A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(1+k*(d+j))) * A(n-j,k) for n > 0.

%e Square array begins:

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

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

%e -1, -16, -256, -4096, ...

%e 0, -713, -531185, -387416393, ...

%e 0, -64711, -4294405135, -281474581032631, ...

%Y Columns k=0..1 give A010815, A294704.

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

%Y Cf. A294583, A294653, A294756.

%K sign,tabl

%O 0,9

%A _Seiichi Manyama_, Nov 07 2017