A309185 (1/6) times the number of n-member subsets of [6n] whose elements sum to a multiple of n.

1, 5, 46, 445, 4751, 54086, 642342, 7861661, 98480332, 1256564755, 16273981758, 213378975958, 2826867619109, 37782552518478, 508840821830546, 6898459216311581, 94070535317459018, 1289430373107971804, 17755914760643605782, 245518560760433579195

Offset: 1

Author

Alois P. Heinz, Jul 15 2019

Keywords

• nonn

Comments

Also (1/5) times the number of n-member subsets of [6n-1] whose elements sum to a multiple of n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..856

Crossrefs

Column k=6 of A309148.

Programs

Maple

with(numtheory):
a:= n-> add(binomial(6*d, d)*(-1)^(n+d)*
        phi(n/d), d in divisors(n))/(6*n):
seq(a(n), n=1..25);

Formula

a(n) = 1/(6n) * Sum_{d|n} binomial(6d,d)*(-1)^(n+d)*phi(n/d).