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A294583 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*x^j)^(j^k).

%I A294583 #17 Nov 05 2017 04:56:56
%S A294583 1,1,-1,1,-1,-1,1,-1,-4,0,1,-1,-16,-5,0,1,-1,-64,-65,-3,1,1,-1,-256,
%T A294583 -665,-79,23,0,1,-1,-1024,-6305,-1575,831,44,1,1,-1,-4096,-58025,
%U A294583 -28255,33335,4789,104,0,1,-1,-16384,-527345,-481623,1323807,411664,15099,70,0
%N A294583 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*x^j)^(j^k).
%H A294583 Seiichi Manyama, <a href="/A294583/b294583.txt">Antidiagonals n = 0..113, flattened</a>
%F A294583 A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(k+1+k*j/d)) * A(n-j,k) for n > 0.
%e A294583 Square array begins:
%e A294583     1,  1,   1,     1,      1, ...
%e A294583    -1, -1,  -1,    -1,     -1, ...
%e A294583    -1, -4, -16,   -64,   -256, ...
%e A294583     0, -5, -65,  -665,  -6305, ...
%e A294583     0, -3, -79, -1575, -28255, ...
%Y A294583 Columns k=0..2 give A010815, A266964, A294584.
%Y A294583 Rows n=0..1 give A000012, (-1)*A000012.
%Y A294583 Cf. A294585.
%K A294583 sign,tabl
%O A294583 0,9
%A A294583 _Seiichi Manyama_, Nov 03 2017