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%I #17 Oct 27 2017 13:11:12
%S 1,1,0,1,-1,0,1,-1,1,0,1,-1,-1,-1,0,1,-1,-1,11,1,0,1,-1,-1,5,-23,-1,0,
%T 1,-1,-1,5,25,-101,1,0,1,-1,-1,5,1,-41,991,-1,0,1,-1,-1,5,1,199,-1769,
%U -1849,1,0,1,-1,-1,5,1,79,-1409,7181,-24751,-1,0,1,-1,-1,5
%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(Product_{j=1..n} (1-x^j) - 1).
%H Seiichi Manyama, <a href="/A294254/b294254.txt">Antidiagonals n = 0..139, flattened</a>
%F B(j,k) is the coefficient of Product_{i=1..k} (1-x^i).
%F A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..min(A000217(k),n)} j*B(j,k)*A(n-j,k)/(n-j)! for n > 0.
%e Square array A(n,k) begins:
%e 1, 1, 1, 1, 1, ...
%e 0, -1, -1, -1, -1, ...
%e 0, 1, -1, -1, -1, ...
%e 0, -1, 11, 5, 5, ...
%e 0, 1, -23, 25, 1, ...
%e 0, -1, -101, -41, 199, ...
%Y Columns k=0..5 give A000007, A033999, A294255, A294256, A294257, A294258.
%Y Rows n=0 gives A000012.
%Y Main diagonal gives A294260.
%Y Cf. A294250.
%K sign,tabl
%O 0,19
%A _Seiichi Manyama_, Oct 26 2017
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