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%I #36 Jan 28 2024 20:56:48
%S 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,
%T 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,
%U 1,1,1,1,1,768,41,10,1,1,1,1,1,1,1,1,1
%N 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.
%e T(8,3) = 2 subsets {1}, {8} of {1..8} with a cube average.
%e Table begins:
%e 1, 1, 1, 1, 1, ...
%e 2, 1, 1, 1, 1, ...
%e 5, 1, 1, 1, 1, ...
%e 8, 2, 1, 1, 1, ...
%e 15, 4, 1, 1, 1, ...
%e 26, 10, 1, 1, 1, ...
%e 45, 20, 1, 1, 1, ...
%e 76, 26, 2, 1, 1, ...
%e 135, 31, 4, 1, 1, ...
%e 238, 35, 10, 1, 1, ...
%e 425, 41, 32, 1, 1, ...
%e 768, 63, 106, 1, 1, ...
%e 1399, 143, 310, 1, 1, ...
%e 2570, 399, 760, 1, 1, ...
%e 4761, 1083, 1520, 1, 1, ...
%e 8856, 2554, 2522, 2, 1, ...
%e 16567, 5078, 3630, 4, 1, ...
%e 31138, 8596, 4708, 10, 1, ...
%e 58733, 12772, 5670, 32, 1, ...
%e 111164, 17222, 6484, 118, 1, ...
%Y Cf. A051293, A369391.
%K tabl,nonn
%O 1,2
%A _Jean-Marc Rebert_, Jan 25 2024