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A047163 Number of nonempty subsets of {1,2,...,n} in which exactly 1/4 of the elements are <= n/2. 2

%I #8 Apr 11 2021 22:15:17

%S 0,0,0,0,2,3,12,16,40,50,110,135,315,392,980,1232,3080,3864,9480,

%T 11850,29040,36300,89870,112519,280423,351351,876603,1098188,2741102,

%U 3433703,8586788,10758608,26965808,33794504,84844280,106344792,267298650,335061789,843098172,1056924666

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

%H Andrew Howroyd, <a href="/A047163/b047163.txt">Table of n, a(n) for n = 1..500</a>

%F a(n) = Sum_{k>=1} binomial(floor(n/2), k)*binomial(ceiling(n/2), 3*k). - _Andrew Howroyd_, Apr 11 2021

%o (PARI) a(n) = {my(m=n\2); sum(k=1, (n-m)\3, binomial(m, k)*binomial(n-m, 3*k))} \\ _Andrew Howroyd_, Apr 11 2021

%Y Cf. A047161, A047164.

%K nonn

%O 1,5

%A _Clark Kimberling_

%E Terms a(35) and beyond from _Andrew Howroyd_, Apr 11 2021

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)