%I #13 Nov 13 2017 13:26:50
%S 1,1,-1,1,-1,-2,1,-1,-4,-7,1,-1,-8,-23,-57,1,-1,-16,-73,-229,-541,1,
%T -1,-32,-227,-927,-2761,-7126,1,-1,-64,-697,-3757,-13969,-42615,
%U -108072,1,-1,-128,-2123,-15207,-70237,-254580,-758499,-1966034
%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of exp(-Sum_{j>0} sigma_k(j)*x^j/j) in powers of x.
%F G.f. of column k: Product_{j>0} (1 - j^j*x^j)^(j^(k-1)).
%e Square array begins:
%e 1, 1, 1, 1, 1, ...
%e -1, -1, -1, -1, -1, ...
%e -2, -4, -8, -16, -32, ...
%e -7, -23, -73, -227, -697, ...
%e -57, -229, -927, -3757, -15207, ...
%e -541, -2761, -13969, -70237, -351361, ...
%Y Columns k=0..2 give A294948, A292312, A294809.
%Y Rows n=0..1 give A000012, (-1)*A000012.
%Y Cf. A294946, A294951.
%K sign,tabl
%O 0,6
%A _Seiichi Manyama_, Nov 11 2017
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