A294761 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: Product_{j>0} 1/(1-j^k*x^j)^(1/j).
1, 1, 1, 1, 1, 3, 1, 1, 4, 11, 1, 1, 6, 18, 59, 1, 1, 10, 36, 132, 339, 1, 1, 18, 84, 384, 900, 2629, 1, 1, 34, 216, 1296, 3240, 10080, 20677, 1, 1, 66, 588, 4704, 13800, 56880, 93240, 202089, 1, 1, 130, 1656, 17712, 64440, 386640, 635040, 1285200, 2066201
Offset: 0
Examples
Square array begins:
1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, ...
3, 4, 6, 10, 18, ...
11, 18, 36, 84, 216, ...
59, 132, 384, 1296, 4704, ...
Links
- Seiichi Manyama, Antidiagonals n = 0..139, flattened
Formula
A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..n} (Sum_{d|j} d^(k*j/d)) * A(n-j,k)/(n-j)! for n > 0.