A309184 (1/5) times the number of n-member subsets of [5n] whose elements sum to a multiple of n.

1, 4, 31, 244, 2126, 19780, 192130, 1922740, 19692535, 205444504, 2175519380, 23322657460, 252631900236, 2760767859784, 30400169157656, 336977765092788, 3757141504436393, 42107201575818028, 474084628585822413, 5359833704140818744, 60823006052351729266

Offset: 1

Author

Alois P. Heinz, Jul 15 2019

Keywords

• nonn

Comments

Also (1/4) times the number of n-member subsets of [5n-1] whose elements sum to a multiple of n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..925

Crossrefs

Column k=5 of A309148.

Programs

Maple

with(numtheory):
a:= n-> add(binomial(5*d, d)*(-1)^(n+d)*
        phi(n/d), d in divisors(n))/(5*n):
seq(a(n), n=1..25);

Formula

a(n) = 1/(5n) * Sum_{d|n} binomial(5d,d)*(-1)^(n+d)*phi(n/d).