A318432 Number of n-element subsets of [4n] whose elements sum to a multiple of n.

1, 4, 12, 76, 460, 3104, 22404, 169152, 1315020, 10460416, 84764512, 697212652, 5805722692, 48847196896, 414623627136, 3546272614976, 30532934225100, 264420681260336, 2301782759539392, 20129523771781288, 176765807152990560, 1558058796052048968

Offset: 0

Author

Marko Riedel, Aug 26 2018

Keywords

• nonn

Links

• Marko Riedel et al., Number of n-element subsets divisible by n

Crossrefs

Cf. A169888, A318431, A318433.

Column k=4 of A304482.

Programs

Maple

with(numtheory); a := n -> `if`(n=0, 1, (-1)^n * 1/n * add(binomial(4*d,d)*(-1)^d*phi(n/d), d in divisors(n)));

PARI

a(n) = if (n, (-1)^n * (1/n) * sumdiv(n, d, binomial(4*d,d)*(-1)^d*eulerphi(n/d)), 1); \\ Michel Marcus, Aug 27 2018

Formula

a(n) = (-1)^n * (1/n) * Sum_{d|n} C(4d,d)*(-1)^d*phi(n/d) for n>0, a(0)=1.