A294289 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(Product_{j=1..n} 1/(1+x^j) - 1).
1, 1, 0, 1, -1, 0, 1, -1, 3, 0, 1, -1, 1, -13, 0, 1, -1, 1, -1, 73, 0, 1, -1, 1, -7, 25, -501, 0, 1, -1, 1, -7, 73, -241, 4051, 0, 1, -1, 1, -7, 49, -421, 1081, -37633, 0, 1, -1, 1, -7, 49, -181, 2641, -3361, 394353, 0, 1, -1, 1, -7, 49, -301, 1561, -32131, 68881
Offset: 0
Examples
Square array A(n,k) begins: 1, 1, 1, 1, 1, ... 0, -1, -1, -1, -1, ... 0, 3, 1, 1, 1, ... 0, -13, -1, -7, -7, ... 0, 73, 25, 73, 49, ... 0, -501, -241, -421, -181, ...
Links
- Seiichi Manyama, Antidiagonals n = 0..139, flattened
Crossrefs
Formula
B(j,k) is the coefficient of Product_{i=1..k} 1/(1+x^i).
A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..n} j*B(j,k)*A(n-j,k)/(n-j)! for n > 0.