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%I #8 Dec 15 2020 18:31:02
%S 0,0,0,1,4,8,20,41,63,126,252,392,844,1780,2800,5995,12545,19595,
%T 41951,88634,138866,299411,636524,997640,2154104,4594244,7201692,
%U 15584085,33355944,52311408,113406028,243374923,381766253,828748052
%N Number of nonempty subsets of {1,2,...,n} in which exactly 1/4 of the elements are <= n/3.
%H Robert Israel, <a href="/A047196/b047196.txt">Table of n, a(n) for n = 1..2000</a>
%F a(n) = Sum_{1<=j<=n/4} binomial(floor(n/3),j)*binomial(n-floor(n/3),3*j). - _Robert Israel_, Dec 15 2020
%p f:= proc(n) local t, k;
%p add(binomial(floor(n/3),k)*binomial(n-floor(n/3),3*k),k=1..n/4)
%p end proc:
%p map(f, [$1..50]); # _Robert Israel_, Dec 15 2020
%K nonn
%O 1,5
%A _Clark Kimberling_
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