A309186 (1/7) times the number of n-member subsets of [7n] whose elements sum to a multiple of n.

1, 6, 64, 734, 9276, 124872, 1753074, 25366334, 375677659, 5667202856, 86775157140, 1345153548200, 21069043965984, 332927798516620, 5301031234085664, 84967018635587774, 1369846562874360887, 22199151535757780226, 361411377745122110422, 5908312923795257322184

Offset: 1

Author

Alois P. Heinz, Jul 15 2019

Keywords

• nonn

Comments

Also (1/6) times the number of n-member subsets of [7n-1] whose elements sum to a multiple of n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..806

Crossrefs

Column k=7 of A309148.

Programs

Maple

with(numtheory):
a:= n-> add(binomial(7*d, d)*(-1)^(n+d)*
        phi(n/d), d in divisors(n))/(7*n):
seq(a(n), n=1..25);

PARI

a(n) = 1/(7*n) * sumdiv(n, d, binomial(7*d,d)*(-1)^(n+d)*eulerphi(n/d)); \\ Michel Marcus, Jul 18 2019

Formula

a(n) = 1/(7n) * Sum_{d|n} binomial(7d,d)*(-1)^(n+d)*phi(n/d).