A294580 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1 - j^k*x^j)^j.
1, 1, -1, 1, -1, -2, 1, -1, -4, -1, 1, -1, -8, -5, 0, 1, -1, -16, -19, -3, 4, 1, -1, -32, -65, -21, 23, 4, 1, -1, -64, -211, -111, 139, 44, 7, 1, -1, -128, -665, -525, 863, 448, 104, 3, 1, -1, -256, -2059, -2343, 5419, 4316, 1414, 70, -2, 1, -1, -512, -6305, -10101, 34103, 40024, 18164, 1206, -93, -9
Offset: 0
Examples
Square array begins:
1, 1, 1, 1, 1, ...
-1, -1, -1, -1, -1, ...
-2, -4, -8, -16, -32, ...
-1, -5, -19, -65, -211, ...
0, -3, -21, -111, -525, ...
Links
- Seiichi Manyama, Antidiagonals n = 0..139, flattened
Crossrefs
Formula
A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(2+k*j/d)) * A(n-j,k) for n > 0.