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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).
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%I #18 Nov 04 2017 10:55:33

%S 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 -65,-13,23,1,1,-1,-64,-211,-63,131,44,13,1,-1,-128,-665,-301,815,497,

%U 104,4,1,-1,-256,-2059,-1383,5195,4840,1149,70,0,1,-1,-512,-6305,-6133,33143,45021,13752,662,-93,2

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

%H Seiichi Manyama, <a href="/A294587/b294587.txt">Antidiagonals n = 0..139, flattened</a>

%F 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 Square array begins:

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

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

%e -2, -4, -8, -16, -32, ...

%e -1, -5, -19, -65, -211, ...

%e -1, -3, -13, -63, -301, ...

%Y Columns k=0..2 give A022661, A266964, A294588.

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

%Y Cf. A283272.

%K sign,tabl

%O 0,6

%A _Seiichi Manyama_, Nov 03 2017