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A309182 (1/3) times the number of n-member subsets of [3n] whose elements sum to a multiple of n.

%I A309182 #9 Jul 16 2019 12:15:23
%S A309182 1,2,10,42,201,1028,5538,30666,173593,1001402,5864750,34769364,
%T A309182 208267320,1258574116,7663720710,46976034378,289628805623,
%U A309182 1794932294978,11175157356522,69864075597442,438403736549145,2760351027094300,17433869214973754,110420300879752980
%N A309182 (1/3) times the number of n-member subsets of [3n] whose elements sum to a multiple of n.
%C A309182 Also (1/2) times the number of n-member subsets of [3n-1] whose elements sum to a multiple of n.
%H A309182 Alois P. Heinz, <a href="/A309182/b309182.txt">Table of n, a(n) for n = 1..1000</a>
%F A309182 a(n) = 1/(3n) * Sum_{d|n} binomial(3d,d)*(-1)^(n+d)*phi(n/d).
%p A309182 with(numtheory):
%p A309182 a:= n-> add(binomial(3*d, d)*(-1)^(n+d)*
%p A309182         phi(n/d), d in divisors(n))/(3*n):
%p A309182 seq(a(n), n=1..25);
%Y A309182 Column k=3 of A309148.
%K A309182 nonn
%O A309182 1,2
%A A309182 _Alois P. Heinz_, Jul 15 2019