A293301 - OEIS

%I #18 Oct 05 2017 11:22:21

%S 1,1,0,1,1,0,1,1,4,0,1,1,3,18,0,1,1,3,12,120,0,1,1,3,13,66,840,0,1,1,

%T 3,13,74,450,7920,0,1,1,3,13,73,510,3510,75600,0,1,1,3,13,73,500,4130,

%U 32760,887040,0,1,1,3,13,73,501,4040,38430,335160,10886400,0,1,1,3

%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} (-1)^j*x^(j*i)/j!).

%H Seiichi Manyama, <a href="/A293301/b293301.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,   4,   3,   3,   3, ...

%e    0,  18,  12,  13,  13, ...

%e    0, 120,  66,  74,  73, ...

%e    0, 840, 450, 510, 500, ...

%Y Columns k=0..2 give A000007, A053529, A293302.

%Y Rows n=0 gives A000012.

%Y Main diagonal gives A000262.

%Y Cf. A293135, A293139, A293299.

%K nonn,tabl,look

%O 0,9

%A _Seiichi Manyama_, Oct 05 2017