Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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