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A294580 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.

%I A294580 #30 Nov 03 2017 19:18:43
%S A294580 1,1,-1,1,-1,-2,1,-1,-4,-1,1,-1,-8,-5,0,1,-1,-16,-19,-3,4,1,-1,-32,
%T A294580 -65,-21,23,4,1,-1,-64,-211,-111,139,44,7,1,-1,-128,-665,-525,863,448,
%U A294580 104,3,1,-1,-256,-2059,-2343,5419,4316,1414,70,-2,1,-1,-512,-6305,-10101,34103,40024,18164,1206,-93,-9
%N A294580 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.
%H A294580 Seiichi Manyama, <a href="/A294580/b294580.txt">Antidiagonals n = 0..139, flattened</a>
%F A294580 A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(2+k*j/d)) * A(n-j,k) for n > 0.
%e A294580 Square array begins:
%e A294580     1,  1,   1,    1,    1, ...
%e A294580    -1, -1,  -1,   -1,   -1, ...
%e A294580    -2, -4,  -8,  -16,  -32, ...
%e A294580    -1, -5, -19,  -65, -211, ...
%e A294580     0, -3, -21, -111, -525, ...
%Y A294580 Columns k=0..2 give A073592, A266964, A294581.
%Y A294580 Rows n=0..3 give A000012, (-1)*A000012, (-1)*A000079(n+1), (-1)*A001047(n+1).
%Y A294580 Cf. A292166, A294582.
%K A294580 sign,tabl,look
%O A294580 0,6
%A A294580 _Seiichi Manyama_, Nov 02 2017