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%I #17 Oct 04 2017 14:07:38
%S 1,1,0,1,-1,0,1,-1,-2,0,1,-1,-1,0,0,1,-1,-1,0,0,0,1,-1,-1,-1,0,120,0,
%T 1,-1,-1,-1,0,0,0,0,1,-1,-1,-1,1,20,180,5040,0,1,-1,-1,-1,1,20,180,0,
%U 0,0,1,-1,-1,-1,1,19,150,1260,10080,0,0,1,-1,-1,-1,1,19
%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. Product_{i>0} Sum_{j=0..k} (-1)^j*x^(j*i)/j!.
%H Seiichi Manyama, <a href="/A293139/b293139.txt">Antidiagonals n = 0..139, flattened</a>
%e Square array begins:
%e 1, 1, 1, 1, 1, ...
%e 0, -1, -1, -1, -1, ...
%e 0, -2, -1, -1, -1, ...
%e 0, 0, 0, -1, -1, ...
%e 0, 0, 0, 0, 1, ...
%e 0, 120, 0, 20, 20, ...
%Y Columns k=0..2 give A000007, A293140, A293141.
%Y Rows n=0 gives A000012.
%Y Main diagonal gives A293116.
%Y Cf. A293135.
%K sign,tabl,look
%O 0,9
%A _Seiichi Manyama_, Oct 01 2017
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