A334568 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals downwards, where column k is the expansion of e.g.f. exp(-Sum_{j=1..k} x^j/j).
1, 1, -1, 1, -1, 1, 1, -1, 0, -1, 1, -1, 0, 2, 1, 1, -1, 0, 0, -2, -1, 1, -1, 0, 0, 6, -6, 1, 1, -1, 0, 0, 0, -6, 16, -1, 1, -1, 0, 0, 0, 24, -24, 20, 1, 1, -1, 0, 0, 0, 0, -24, -120, -132, -1, 1, -1, 0, 0, 0, 0, 120, -120, 540, -28, 1, 1, -1, 0, 0, 0, 0, 0, -120, -720, 1764, 1216, -1
Offset: 0
Examples
Square array begins: 1, 1, 1, 1, 1, 1, 1, ... -1, -1, -1, -1, -1, -1, -1, ... 1, 0, 0, 0, 0, 0, 0, ... -1, 2, 0, 0, 0, 0, 0, ... 1, -2, 6, 0, 0, 0, 0, ... -1, -6, -6, 24, 0, 0, 0, ... 1, 16, -24, -24, 120, 0, 0, ... -1, 20, -120, -120, -120, 720, 0, ... 1, -132, 540, -720, -720, -720, 5040, ...
Links
- Seiichi Manyama, Antidiagonals n = 0..139, flattened
Formula
A(0,k) = 1 and A(n,k) = - (n-1)! * Sum_{j=1..min(k,n)} A(n-j,k)/(n-j)!.