A309187 - OEIS

%I #10 Jul 18 2019 11:38:56

%S 1,7,85,1127,16451,255619,4141383,69159399,1182125128,20581143157,

%T 363704640476,6506965279907,117626432708864,2145180354493281,

%U 39421026305282660,729242353169440743,13568988503585900648,253785064585174334488,4768543107831461199897

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

%C Also (1/7) times the number of n-member subsets of [8n-1] whose elements sum to a multiple of n.

%H Alois P. Heinz, <a href="/A309187/b309187.txt">Table of n, a(n) for n = 1..768</a>

%F a(n) = 1/(8n) * Sum_{d|n} binomial(8d,d)*(-1)^(n+d)*phi(n/d).

%p with(numtheory):

%p a:= n-> add(binomial(8*d, d)*(-1)^(n+d)*

%p         phi(n/d), d in divisors(n))/(8*n):

%p seq(a(n), n=1..25);

%o (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 Column k=8 of A309148.

%K nonn

%O 1,2

%A _Alois P. Heinz_, Jul 15 2019