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A294699 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.

%I A294699 #19 Nov 08 2017 12:02:41
%S A294699 1,1,-1,1,-1,-1,1,-1,-16,0,1,-1,-256,-713,0,1,-1,-4096,-531185,-64711,
%T A294699 1,1,-1,-65536,-387416393,-4294405135,-9688521,0,1,-1,-1048576,
%U A294699 -282429470945,-281474581032631,-95363000655153,-2165724176,1,1
%N A294699 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 A294699 Seiichi Manyama, <a href="/A294699/b294699.txt">Antidiagonals n = 0..38, flattened</a>
%F A294699 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 A294699 Square array begins:
%e A294699     1,      1,           1,                1, ...
%e A294699    -1,     -1,          -1,               -1, ...
%e A294699    -1,    -16,        -256,            -4096, ...
%e A294699     0,   -713,     -531185,       -387416393, ...
%e A294699     0, -64711, -4294405135, -281474581032631, ...
%Y A294699 Columns k=0..1 give A010815, A294704.
%Y A294699 Rows n=0..1 give A000012, (-1)*A000012.
%Y A294699 Cf. A294583, A294653, A294756.
%K A294699 sign,tabl
%O A294699 0,9
%A A294699 _Seiichi Manyama_, Nov 07 2017