A047165 - OEIS

%I #8 Apr 11 2021 22:15:29

%S 0,0,0,0,0,0,3,4,20,25,75,90,210,245,511,588,1260,1458,3510,4125,

%T 10725,12705,32835,38830,96382,113399,273273,320411,770315,903175,

%U 2208115,2594540,6451500,7594920,18990768,22366458,55715562,65579982,162488703,191126529

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

%H Andrew Howroyd, <a href="/A047165/b047165.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), 4*k). - _Andrew Howroyd_, Apr 11 2021

%o (PARI) a(n) = {my(m=n\2); sum(k=1, (n-m)\4, binomial(m, k)*binomial(n-m, 4*k))} \\ _Andrew Howroyd_, Apr 11 2021

%Y Cf. A047161, A047166, A047167, A047168.

%K nonn

%O 1,7

%A _Clark Kimberling_

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