A309183 (1/4) times the number of n-member subsets of [4n] whose elements sum to a multiple of n.

1, 3, 19, 115, 776, 5601, 42288, 328755, 2615104, 21191128, 174303163, 1451430673, 12211799224, 103655906784, 886568153744, 7633233556275, 66105170315084, 575445689884848, 5032380942945322, 44191451788247640, 389514699013012242, 3444925385161998521

Offset: 1

Author

Alois P. Heinz, Jul 15 2019

Keywords

• nonn

Comments

Also (1/3) times the number of n-member subsets of [4n-1] whose elements sum to a multiple of n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Column k=4 of A309148.

Programs

Maple

with(numtheory):
a:= n-> add(binomial(4*d, d)*(-1)^(n+d)*
        phi(n/d), d in divisors(n))/(4*n):
seq(a(n), n=1..25);

Formula

a(n) = 1/(4n) * Sum_{d|n} binomial(4d,d)*(-1)^(n+d)*phi(n/d).