A293019 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.

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, 0, 0, -24, 100, -95, -9, 1, 0, 0, 0, -24, -60, 570, -414, 50, 1, 0, 0, 0, 0, -120, 240, 798, 49, 267, 1, 0, 0, 0, 0, -120, -360, 4830, -15176, 10088, 413, 1, 0, 0

Offset: 0

Author

Seiichi Manyama, Sep 28 2017

Keywords

• sign
• tabl

Examples

			Square array begins:
    1,  1,  1,   1,   1, ...
   -1, -1,  0,   0,   0, ...
    0, -1, -2,   0,   0, ...
    1,  2, -6,  -6,   0, ...
    1,  9,  0, -24, -24, ...
		

Links

• Seiichi Manyama, Antidiagonals n = 0..139, flattened

Crossrefs

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

Rows n=0 gives A000012.

Cf. A292978, A293015.