%I #12 Sep 25 2022 11:03:55
%S 1,1,2,4,9,13,20,38,71,119,206,384,713,1285,2356,4428,8331,15569,
%T 29270,55582,105717,200847,382808,732744,1404667,2694391,5178186,
%U 9973416,19233457,37125547,71754692,138871244,269038123,521666967,1012485750,1966957674,3824314685
%N Number of nonempty subsets of {1..n} whose elements have an odd average.
%F a(n) = A051293(n) - A357356(n). - _Michael S. Branicky_, Sep 25 2022
%e a(6) = 13 subsets: {1}, {3}, {5}, {1, 5}, {2, 4}, {4, 6}, {1, 2, 6}, {1, 3, 5}, {2, 3, 4}, {4, 5, 6}, {1, 2, 3, 6}, {1, 2, 4, 5} and {1, 2, 3, 4, 5}.
%o (Python)
%o from functools import lru_cache
%o def cond(s, c): q, r = divmod(s, c); return r == 0 and q&1
%o @lru_cache(maxsize=None)
%o def b(n, s, c):
%o if n == 0: return int (c > 0 and cond(s, c))
%o return b(n-1, s, c) + b(n-1, s+n, c+1)
%o a = lambda n: b(n, 0, 0)
%o print([a(n) for n in range(1, 51)]) # _Michael S. Branicky_, Sep 25 2022
%Y Cf. A051293, A309160, A357356.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, Sep 25 2022
%E a(24)-a(37) from _Michael S. Branicky_, Sep 25 2022