A047170 - OEIS

%I #8 Apr 11 2021 22:16:07

%S 0,0,0,0,0,0,0,0,0,5,6,36,42,147,168,448,504,1134,1260,2565,2827,5687,

%T 6270,13860,15444,39039,44044,119119,135135,360815,408968,1039808,

%U 1174224,2842604,3197904,7515054,8436114,19773414,22203020,53093125,59750649,146794494

%N Number of nonempty subsets of {1,2,...,n} in which exactly 5/6 of the elements are <= n/2.

%H Andrew Howroyd, <a href="/A047170/b047170.txt">Table of n, a(n) for n = 1..500</a>

%F a(n) = Sum_{k>=1} binomial(floor(n/2), 5*k)*binomial(ceiling(n/2), k). - _Andrew Howroyd_, Apr 11 2021

%o (PARI) a(n) = {my(m=n\2); sum(k=1, m\5, binomial(m, 5*k)*binomial(n-m, k))} \\ _Andrew Howroyd_, Apr 11 2021

%Y Cf. A047169.

%K nonn

%O 1,10

%A _Clark Kimberling_

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