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A294254 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).

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