A294118 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(k*((1+x)^k - 1)).
1, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 9, 20, 1, 0, 1, 16, 99, 112, 1, 0, 1, 25, 304, 1233, 688, 1, 0, 1, 36, 725, 6496, 16929, 4544, 1, 0, 1, 49, 1476, 23425, 152416, 251829, 31936, 1, 0, 1, 64, 2695, 66816, 826225, 3867136, 4012011, 236800, 1, 0, 1, 81, 4544, 162337
Offset: 0
Examples
Square array A(n,k) begins: 1, 1, 1, 1, 1, ... 0, 1, 4, 9, 16, ... 0, 1, 20, 99, 304, ... 0, 1, 112, 1233, 6496, ... 0, 1, 688, 16929, 152416, ... 0, 1, 4544, 251829, 3867136, ...
Links
- Seiichi Manyama, Antidiagonals n = 0..139, flattened
Crossrefs
Formula
A(0,k) = 1 and A(n,k) = k^2 * (n-1)! * Sum_{j=1..min(k,n)} binomial(k-1,j-1)*A(n-j,k)/(n-j)! for n > 0.