A369526 Table read by upward antidiagonals: T(n,k) = number of nonempty subsets of {1..n} for which the average is the k-th power of an integer.
1, 2, 1, 5, 1, 1, 8, 1, 1, 1, 15, 2, 1, 1, 1, 26, 4, 1, 1, 1, 1, 45, 10, 1, 1, 1, 1, 1, 76, 20, 1, 1, 1, 1, 1, 1, 135, 26, 1, 1, 1, 1, 1, 1, 1, 238, 31, 2, 1, 1, 1, 1, 1, 1, 1, 425, 35, 4, 1, 1, 1, 1, 1, 1, 1, 1, 768, 41, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 1
Examples
T(8,3) = 2 subsets {1}, {8} of {1..8} with a cube average.
Table begins:
1, 1, 1, 1, 1, ...
2, 1, 1, 1, 1, ...
5, 1, 1, 1, 1, ...
8, 2, 1, 1, 1, ...
15, 4, 1, 1, 1, ...
26, 10, 1, 1, 1, ...
45, 20, 1, 1, 1, ...
76, 26, 2, 1, 1, ...
135, 31, 4, 1, 1, ...
238, 35, 10, 1, 1, ...
425, 41, 32, 1, 1, ...
768, 63, 106, 1, 1, ...
1399, 143, 310, 1, 1, ...
2570, 399, 760, 1, 1, ...
4761, 1083, 1520, 1, 1, ...
8856, 2554, 2522, 2, 1, ...
16567, 5078, 3630, 4, 1, ...
31138, 8596, 4708, 10, 1, ...
58733, 12772, 5670, 32, 1, ...
111164, 17222, 6484, 118, 1, ...