A318431 Number of n-element subsets of [3n] whose elements sum to a multiple of n.

1, 3, 6, 30, 126, 603, 3084, 16614, 91998, 520779, 3004206, 17594250, 104308092, 624801960, 3775722348, 22991162130, 140928103134, 868886416869, 5384796884934, 33525472069566, 209592226792326, 1315211209647435, 8281053081282900, 52301607644921262

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, A318432, A318433.

Column k=3 of A304482.

Programs

Maple

with(numtheory); a := n -> `if`(n=0, 1, (-1)^n * 1/n * add(binomial(3*d,d)*(-1)^d*phi(n/d), d in divisors(n)));

PARI

a(n) = if (n, (-1)^n * (1/n) * sumdiv(n, d, binomial(3*d,d)*(-1)^d*eulerphi(n/d)), 1); \\ Michel Marcus, Aug 27 2018

Formula

a(n) = (-1)^n * (1/n) * Sum_{d|n} C(3d,d)*(-1)^d*phi(n/d) for n>0, a(0)=1.