A318431 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..23.

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

FORMULA

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

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)));

PROG

(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