cp's OEIS Frontend

A309188 (1/9) times the number of n-member subsets of [9n] whose elements sum to a multiple of n.

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