A294254 - 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