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A048000 Number of nonempty subsets of {1,2,...,n} in which exactly 4/5 of the elements are <= n/3. 1

%I #13 Jun 10 2019 00:24:46

%S 0,0,0,0,0,0,0,0,0,0,0,8,9,10,50,55,60,180,195,210,490,525,560,1240,

%T 1326,1413,3645,3933,4230,12750,13860,15015,45375,49335,53460,150524,

%U 163175,176345,470665,509067,549094,1461278,1580761

%N Number of nonempty subsets of {1,2,...,n} in which exactly 4/5 of the elements are <= n/3.

%H Robert Israel, <a href="/A048000/b048000.txt">Table of n, a(n) for n = 1..5711</a>

%F a(n) = Sum_{k=1..floor(n/5)} binomial(floor(n/3), 4*k)*binomial(ceiling(2*n/3), k). - _Robert Israel_, Feb 05 2017

%p f:= proc(n) local k;

%p add(binomial(floor(n/3),4*k/5)*binomial(n-floor(n/3),k/5),k=5..n,5)

%p end proc:

%p map(f, [$1..60]); # _Robert Israel_, Feb 05 2017

%o (PARI) a(n)=sum(k=1,n\5, binomial(n\3, 4*k)*binomial(ceil(2*n/3),k)) \\ _Charles R Greathouse IV_, Feb 05 2017

%K nonn

%O 1,12

%A _Clark Kimberling_

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Last modified March 3 16:49 EST 2024. Contains 370512 sequences. (Running on oeis4.)