A283675 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-x^j)^(j^(k*j)) in powers of x.
1, 1, -1, 1, -1, -1, 1, -1, -4, 0, 1, -1, -16, -23, 0, 1, -1, -64, -713, -223, 1, 1, -1, -256, -19619, -64687, -2767, 0, 1, -1, -1024, -531185, -16755517, -9688545, -42268, 1, 1, -1, -4096, -14347883, -4294403215, -30499543213, -2165715003, -759008, 0, 1, -1, -16384
Offset: 0
Examples
Square array begins: 1, 1, 1, 1, ... -1, -1, -1, -1, ... -1, -4, -16, -64, ... 0, -23, -713, -19619, ... 0, -223, -64687, -16755517, ...
Links
- Seiichi Manyama, Antidiagonals n = 0..52, flattened
Crossrefs
Formula
G.f. of column k: Product_{j>=1} (1-x^j)^(j^(k*j)).
A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(k*d+1)) * A(n-j,k) for n > 0. - Seiichi Manyama, Nov 04 2017