A309189 (1/10) times the number of n-member subsets of [10n] whose elements sum to a multiple of n.

1, 9, 136, 2289, 42376, 834336, 17125354, 362345361, 7847250409, 173103073384, 3875837737520, 87857163416064, 2012268157890524, 46497242493163450, 1082614775186919136, 25374686712458407441, 598217593341171422090, 14176230568946364963825

Offset: 1

Author

Alois P. Heinz, Jul 15 2019

Keywords

• nonn

Comments

Also (1/9) times the number of n-member subsets of [10n-1] whose elements sum to a multiple of n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..712

Crossrefs

Column k=10 of A309148.

Programs

Maple

with(numtheory):
a:= n-> add(binomial(10*d, d)*(-1)^(n+d)*
        phi(n/d), d in divisors(n))/(10*n):
seq(a(n), n=1..25);

PARI

a(n) = 1/(10*n) * sumdiv(n, d, binomial(10*d, d)*(-1)^(n+d)*eulerphi(n/d)); \\ Michel Marcus, Jul 20 2019

Formula

a(n) = 1/(10n) * Sum_{d|n} binomial(10d,d)*(-1)^(n+d)*phi(n/d).