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A294289 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/(1+x^j) - 1).

%I A294289 #15 Oct 27 2017 13:10:51
%S A294289 1,1,0,1,-1,0,1,-1,3,0,1,-1,1,-13,0,1,-1,1,-1,73,0,1,-1,1,-7,25,-501,
%T A294289 0,1,-1,1,-7,73,-241,4051,0,1,-1,1,-7,49,-421,1081,-37633,0,1,-1,1,-7,
%U A294289 49,-181,2641,-3361,394353,0,1,-1,1,-7,49,-301,1561,-32131,68881
%N A294289 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/(1+x^j) - 1).
%H A294289 Seiichi Manyama, <a href="/A294289/b294289.txt">Antidiagonals n = 0..139, flattened</a>
%F A294289 B(j,k) is the coefficient of Product_{i=1..k} 1/(1+x^i).
%F A294289 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 A294289 Square array A(n,k) begins:
%e A294289    1,    1,    1,    1,    1, ...
%e A294289    0,   -1,   -1,   -1,   -1, ...
%e A294289    0,    3,    1,    1,    1, ...
%e A294289    0,  -13,   -1,   -7,   -7, ...
%e A294289    0,   73,   25,   73,   49, ...
%e A294289    0, -501, -241, -421, -181, ...
%Y A294289 Columns k=0..5 give A000007, A293125, A294290, A294291, A294292, A294293.
%Y A294289 Rows n=0 gives A000012.
%Y A294289 Main diagonal gives A294261.
%Y A294289 Cf. A294212.
%K A294289 sign,tabl
%O A294289 0,9
%A A294289 _Seiichi Manyama_, Oct 27 2017