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%I #11 Jul 18 2019 10:14:03
%S 1,3,19,115,776,5601,42288,328755,2615104,21191128,174303163,
%T 1451430673,12211799224,103655906784,886568153744,7633233556275,
%U 66105170315084,575445689884848,5032380942945322,44191451788247640,389514699013012242,3444925385161998521
%N (1/4) times the number of n-member subsets of [4n] whose elements sum to a multiple of n.
%C Also (1/3) times the number of n-member subsets of [4n-1] whose elements sum to a multiple of n.
%H Alois P. Heinz, <a href="/A309183/b309183.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = 1/(4n) * Sum_{d|n} binomial(4d,d)*(-1)^(n+d)*phi(n/d).
%p with(numtheory):
%p a:= n-> add(binomial(4*d, d)*(-1)^(n+d)*
%p phi(n/d), d in divisors(n))/(4*n):
%p seq(a(n), n=1..25);
%Y Column k=4 of A309148.
%K nonn
%O 1,2
%A _Alois P. Heinz_, Jul 15 2019