A293299 - OEIS

%I #17 Oct 05 2017 11:22:13

%S 1,1,0,1,-1,0,1,-1,0,0,1,-1,-1,-6,0,1,-1,-1,0,24,0,1,-1,-1,-1,-6,-120,

%T 0,1,-1,-1,-1,2,30,720,0,1,-1,-1,-1,1,10,270,-5040,0,1,-1,-1,-1,1,20,

%U 170,0,80640,0,1,-1,-1,-1,1,19,140,1050,2520,-725760,0,1,-1

%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. Product_{i>0} 1/(Sum_{j=0..k} x^(j*i)/j!).

%H Seiichi Manyama, <a href="/A293299/b293299.txt">Antidiagonals n = 0..139, flattened</a>

%e Square array begins:

%e    1,    1,  1,  1,  1, ...

%e    0,   -1, -1, -1, -1, ...

%e    0,    0, -1, -1, -1, ...

%e    0,   -6,  0, -1, -1, ...

%e    0,   24, -6,  2,  1, ...

%e    0, -120, 30, 10, 20, ...

%Y Columns k=0..1 give A000007, A293300.

%Y Rows n=0 gives A000012.

%Y Main diagonal gives A293116.

%Y Cf. A293135, A293301.

%K sign,tabl

%O 0,14

%A _Seiichi Manyama_, Oct 05 2017