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A294587 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1 - j*x^j)^(j^k).

%I A294587 #18 Nov 04 2017 10:55:33
%S A294587 1,1,-1,1,-1,-2,1,-1,-4,-1,1,-1,-8,-5,-1,1,-1,-16,-19,-3,5,1,-1,-32,
%T A294587 -65,-13,23,1,1,-1,-64,-211,-63,131,44,13,1,-1,-128,-665,-301,815,497,
%U A294587 104,4,1,-1,-256,-2059,-1383,5195,4840,1149,70,0,1,-1,-512,-6305,-6133,33143,45021,13752,662,-93,2
%N A294587 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1 - j*x^j)^(j^k).
%H A294587 Seiichi Manyama, <a href="/A294587/b294587.txt">Antidiagonals n = 0..139, flattened</a>
%F A294587 A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(k+1+j/d)) * A(n-j,k) for n > 0.
%e A294587 Square array begins:
%e A294587     1,  1,   1,   1,    1, ...
%e A294587    -1, -1,  -1,  -1,   -1, ...
%e A294587    -2, -4,  -8, -16,  -32, ...
%e A294587    -1, -5, -19, -65, -211, ...
%e A294587    -1, -3, -13, -63, -301, ...
%Y A294587 Columns k=0..2 give A022661, A266964, A294588.
%Y A294587 Rows n=0..1 give A000012, (-1)*A000012.
%Y A294587 Cf. A283272.
%K A294587 sign,tabl
%O A294587 0,6
%A A294587 _Seiichi Manyama_, Nov 03 2017