A294212 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, 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, 5, 13, 0, 1, 1, 5, 25, 73, 0, 1, 1, 5, 31, 193, 501, 0, 1, 1, 5, 31, 241, 1601, 4051, 0, 1, 1, 5, 31, 265, 2261, 16741, 37633, 0, 1, 1, 5, 31, 265, 2501, 25501, 190345, 394353, 0, 1, 1, 5, 31, 265, 2621, 29461, 319915, 2509025
Offset: 0
Examples
Square array B(j,k) begins: 1, 1, 1, 1, 1, ... 0, 1, 1, 1, 1, ... 0, 1, 2, 2, 2, ... 0, 1, 2, 3, 3, ... 0, 1, 3, 4, 5, ... 0, 1, 3, 5, 6, ... Square array A(n,k) begins: 1, 1, 1, 1, 1, ... 0, 1, 1, 1, 1, ... 0, 3, 5, 5, 5, ... 0, 13, 25, 31, 31, ... 0, 73, 193, 241, 265, ... 0, 501, 1601, 2261, 2501, ...
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.