A294188 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/(1-x)^k - 1)).
1, 1, 0, 1, 1, 0, 1, 4, 3, 0, 1, 9, 28, 13, 0, 1, 16, 117, 256, 73, 0, 1, 25, 336, 1881, 2848, 501, 0, 1, 36, 775, 8416, 35505, 37024, 4051, 0, 1, 49, 1548, 27925, 241696, 763209, 547936, 37633, 0, 1, 64, 2793, 75888, 1134025, 7769856, 18309861, 9064192
Offset: 0
Examples
Square array A(n,k) begins: 1, 1, 1, 1, 1, ... 0, 1, 4, 9, 16, ... 0, 3, 28, 117, 336, ... 0, 13, 256, 1881, 8416, ... 0, 73, 2848, 35505, 241696, ... 0, 501, 37024, 763209, 7769856, ...
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..n} binomial(j+k-1,k)*A(n-j,k)/(n-j)! for n > 0.