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A309187 (1/8) times the number of n-member subsets of [8n] whose elements sum to a multiple of n.

%I A309187 #10 Jul 18 2019 11:38:56
%S A309187 1,7,85,1127,16451,255619,4141383,69159399,1182125128,20581143157,
%T A309187 363704640476,6506965279907,117626432708864,2145180354493281,
%U A309187 39421026305282660,729242353169440743,13568988503585900648,253785064585174334488,4768543107831461199897
%N A309187 (1/8) times the number of n-member subsets of [8n] whose elements sum to a multiple of n.
%C A309187 Also (1/7) times the number of n-member subsets of [8n-1] whose elements sum to a multiple of n.
%H A309187 Alois P. Heinz, <a href="/A309187/b309187.txt">Table of n, a(n) for n = 1..768</a>
%F A309187 a(n) = 1/(8n) * Sum_{d|n} binomial(8d,d)*(-1)^(n+d)*phi(n/d).
%p A309187 with(numtheory):
%p A309187 a:= n-> add(binomial(8*d, d)*(-1)^(n+d)*
%p A309187         phi(n/d), d in divisors(n))/(8*n):
%p A309187 seq(a(n), n=1..25);
%o A309187 (PARI) a(n) = 1/(8*n) * sumdiv(n, d, binomial(8*d,d)*(-1)^(n+d)*eulerphi(n/d)); \\ _Michel Marcus_, Jul 18 2019
%Y A309187 Column k=8 of A309148.
%K A309187 nonn
%O A309187 1,2
%A A309187 _Alois P. Heinz_, Jul 15 2019