A293019 - OEIS

%I #12 Sep 30 2017 04:39:45

%S 1,1,-1,1,-1,0,1,0,-1,1,1,0,-2,2,1,1,0,0,-6,9,-2,1,0,0,-6,0,4,-9,1,0,

%T 0,0,-24,100,-95,-9,1,0,0,0,-24,-60,570,-414,50,1,0,0,0,0,-120,240,

%U 798,49,267,1,0,0,0,0,-120,-360,4830,-15176,10088,413,1,0,0

%N Square array A(n,k), n>=0, k>=0, read by antidiagonals, where A(0,k) = 1 and A(n,k) = - k! * Sum_{i=0..n-1} binomial(n-1,i) * binomial(i+1,k) * A(n-1-i,k) for n > 0.

%H Seiichi Manyama, <a href="/A293019/b293019.txt">Antidiagonals n = 0..139, flattened</a>

%e Square array begins:

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

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

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

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

%e     1,  9,  0, -24, -24, ...

%Y Columns k=0-4 give: A000587, A292952, A293016, A293017, A293018.

%Y Rows n=0 gives A000012.

%Y Cf. A292978, A293015.

%K sign,tabl

%O 0,13

%A _Seiichi Manyama_, Sep 28 2017