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%I #33 Oct 29 2017 06:41:56
%S 1,1,0,1,1,0,1,1,3,0,1,1,5,13,0,1,1,5,25,73,0,1,1,5,31,193,501,0,1,1,
%T 5,31,241,1601,4051,0,1,1,5,31,265,2261,16741,37633,0,1,1,5,31,265,
%U 2501,25501,190345,394353,0,1,1,5,31,265,2621,29461,319915,2509025
%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f.: exp(Product_{j=1..n} 1/(1-x^j) - 1).
%H Seiichi Manyama, <a href="/A294212/b294212.txt">Antidiagonals n = 0..139, flattened</a>
%F B(j,k) is the coefficient of Product_{i=1..k} 1/(1-x^i).
%F A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..n} j*B(j,k)*A(n-j,k)/(n-j)! for n > 0.
%e Square array B(j,k) begins:
%e 1, 1, 1, 1, 1, ...
%e 0, 1, 1, 1, 1, ...
%e 0, 1, 2, 2, 2, ...
%e 0, 1, 2, 3, 3, ...
%e 0, 1, 3, 4, 5, ...
%e 0, 1, 3, 5, 6, ...
%e Square array A(n,k) begins:
%e 1, 1, 1, 1, 1, ...
%e 0, 1, 1, 1, 1, ...
%e 0, 3, 5, 5, 5, ...
%e 0, 13, 25, 31, 31, ...
%e 0, 73, 193, 241, 265, ...
%e 0, 501, 1601, 2261, 2501, ...
%Y Columns k=0..5 give A000007, A000262, A294213, A294214, A294215, A294216.
%Y Rows n=0 gives A000012.
%Y Main diagonal gives A058892.
%Y Cf. A058398, A294250, A294254, A294289.
%K nonn,tabl
%O 0,9
%A _Seiichi Manyama_, Oct 25 2017