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A309185 (1/6) times the number of n-member subsets of [6n] whose elements sum to a multiple of n.

%I A309185 #10 Jul 18 2019 10:15:43
%S A309185 1,5,46,445,4751,54086,642342,7861661,98480332,1256564755,16273981758,
%T A309185 213378975958,2826867619109,37782552518478,508840821830546,
%U A309185 6898459216311581,94070535317459018,1289430373107971804,17755914760643605782,245518560760433579195
%N A309185 (1/6) times the number of n-member subsets of [6n] whose elements sum to a multiple of n.
%C A309185 Also (1/5) times the number of n-member subsets of [6n-1] whose elements sum to a multiple of n.
%H A309185 Alois P. Heinz, <a href="/A309185/b309185.txt">Table of n, a(n) for n = 1..856</a>
%F A309185 a(n) = 1/(6n) * Sum_{d|n} binomial(6d,d)*(-1)^(n+d)*phi(n/d).
%p A309185 with(numtheory):
%p A309185 a:= n-> add(binomial(6*d, d)*(-1)^(n+d)*
%p A309185         phi(n/d), d in divisors(n))/(6*n):
%p A309185 seq(a(n), n=1..25);
%Y A309185 Column k=6 of A309148.
%K A309185 nonn
%O A309185 1,2
%A A309185 _Alois P. Heinz_, Jul 15 2019