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%I #9 Jul 19 2019 04:24:39
%S 1,8,109,1640,27151,478232,8782075,166237160,3220837534,63562714008,
%T 1273237637706,25820645555000,529080420540114,10937268134114568,
%U 227824992158991334,4777204094770874856,100757627271124231383,2136117417345649876112,45496022230420668679932
%N (1/9) times the number of n-member subsets of [9n] whose elements sum to a multiple of n.
%C Also (1/8) times the number of n-member subsets of [9n-1] whose elements sum to a multiple of n.
%H Alois P. Heinz, <a href="/A309188/b309188.txt">Table of n, a(n) for n = 1..737</a>
%F a(n) = 1/(9n) * Sum_{d|n} binomial(9d,d)*(-1)^(n+d)*phi(n/d).
%p with(numtheory):
%p a:= n-> add(binomial(9*d, d)*(-1)^(n+d)*
%p phi(n/d), d in divisors(n))/(9*n):
%p seq(a(n), n=1..25);
%o (PARI) a(n) = 1/(9*n) * sumdiv(n, d, binomial(9*d, d)*(-1)^(n+d)*eulerphi(n/d)); \\ _Michel Marcus_, Jul 19 2019
%Y Column k=9 of A309148.
%K nonn
%O 1,2
%A _Alois P. Heinz_, Jul 15 2019
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