A318432 - OEIS

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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

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

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

FORMULA

a(n) = (-1)^n * (1/n) * Sum_{d|n} C(4d,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(4*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(4*d, d)*(-1)^d*eulerphi(n/d)), 1); \\ Michel Marcus, Aug 27 2018