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

1, 7, 85, 1127, 16451, 255619, 4141383, 69159399, 1182125128, 20581143157, 363704640476, 6506965279907, 117626432708864, 2145180354493281, 39421026305282660, 729242353169440743, 13568988503585900648, 253785064585174334488, 4768543107831461199897

Offset: 1

Author

Alois P. Heinz, Jul 15 2019

Keywords

• nonn

Comments

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..768

Crossrefs

Column k=8 of A309148.

Programs

Maple

with(numtheory):
a:= n-> add(binomial(8*d, d)*(-1)^(n+d)*
        phi(n/d), d in divisors(n))/(8*n):
seq(a(n), n=1..25);

PARI

a(n) = 1/(8*n) * sumdiv(n, d, binomial(8*d,d)*(-1)^(n+d)*eulerphi(n/d)); \\ Michel Marcus, Jul 18 2019

Formula

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