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%I #17 Oct 05 2017 11:22:13
%S 1,1,0,1,-1,0,1,-1,0,0,1,-1,-1,-6,0,1,-1,-1,0,24,0,1,-1,-1,-1,-6,-120,
%T 0,1,-1,-1,-1,2,30,720,0,1,-1,-1,-1,1,10,270,-5040,0,1,-1,-1,-1,1,20,
%U 170,0,80640,0,1,-1,-1,-1,1,19,140,1050,2520,-725760,0,1,-1
%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} 1/(Sum_{j=0..k} x^(j*i)/j!).
%H Seiichi Manyama, <a href="/A293299/b293299.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, 0, -1, -1, -1, ...
%e 0, -6, 0, -1, -1, ...
%e 0, 24, -6, 2, 1, ...
%e 0, -120, 30, 10, 20, ...
%Y Columns k=0..1 give A000007, A293300.
%Y Rows n=0 gives A000012.
%Y Main diagonal gives A293116.
%Y Cf. A293135, A293301.
%K sign,tabl
%O 0,14
%A _Seiichi Manyama_, Oct 05 2017