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%I #9 Apr 11 2021 22:15:01
%S 0,0,1,2,6,9,21,30,70,100,235,335,791,1127,2681,3822,9150,13050,31401,
%T 44802,108262,154517,374715,534963,1301235,1858155,4531423,6472167,
%U 15818791,22597759,55339849,79067374,193962894,277164294,680963509,973184312,2394289028,3422117189
%N Number of nonempty subsets of {1,2,...,n} in which exactly 1/3 of the elements are <= n/2.
%H Andrew Howroyd, <a href="/A047161/b047161.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{k>=1} binomial(floor(n/2), k)*binomial(ceiling(n/2), 2*k). - _Andrew Howroyd_, Apr 11 2021
%o (PARI) a(n) = {my(m=n\2); sum(k=1, (n+1)\4, binomial(m, k)*binomial(n-m, 2*k))} \\ _Andrew Howroyd_, Apr 11 2021
%Y Cf. A014495, A047162.
%K nonn
%O 1,4
%A _Clark Kimberling_
%E Terms a(35) and beyond from _Andrew Howroyd_, Apr 11 2021
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