A293908 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(Sum_{j>=1} j^(k-1)*A000009(j)*x^j).
1, 1, 1, 1, 1, 2, 1, 1, 3, 8, 1, 1, 5, 19, 38, 1, 1, 9, 49, 121, 238, 1, 1, 17, 133, 409, 1041, 1828, 1, 1, 33, 373, 1441, 4841, 10651, 16096, 1, 1, 65, 1069, 5233, 23601, 66541, 121843, 160604, 1, 1, 129, 3109, 19441, 119441, 442681, 1006825, 1575729, 1826684, 1, 1
Offset: 0
Examples
Square array begins:
1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, ...
2, 3, 5, 9, 17, ...
8, 19, 49, 133, 373, ...
38, 121, 409, 1411, 5233, ...
238, 1041, 4841, 23601, 119441, ...
Links
- Seiichi Manyama, Antidiagonals n = 0..139, flattened
Formula
A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..n} j^k*A000009(j)*A(n-j,k)/(n-j)! for n > 0.