A293015 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where A(0,k) = 1 and A(n,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, -1, 2, 1, 1, 0, 0, -3, 9, -2, 1, 0, 0, -1, -3, 4, -9, 1, 0, 0, 0, -4, 20, -95, -9, 1, 0, 0, 0, -1, -10, 150, -414, 50, 1, 0, 0, 0, 0, -5, -10, 504, 49, 267, 1, 0, 0, 0, 0, -1, -15, 105, -343, 10088, 413, 1, 0, 0, 0, 0, 0, -6

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, -1,  0,  0, ...
    1,  2, -3, -1,  0, ...
    1,  9, -3, -4, -1, ...
		

Links

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

Crossrefs

Columns k=0-4 give: A000587, A292952, A292953, A292954, A292955.

Rows n=0 gives A000012.

Cf. A145460.