A318433 Number of n-element subsets of [5n] whose elements sum to a multiple of n.

1, 5, 20, 155, 1220, 10630, 98900, 960650, 9613700, 98462675, 1027222520, 10877596900, 116613287300, 1263159501180, 13803839298920, 152000845788280, 1684888825463940, 18785707522181965, 210536007879090140, 2370423142929112065, 26799168520704093720

Offset

0,2

Links

Table of n, a(n) for n=0..20.

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

Formula

a(n) = (-1)^n * (1/n) * Sum_{d|n} C(5d,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(5*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(5*d, d)*(-1)^d*eulerphi(n/d)), 1); \\ Michel Marcus, Aug 27 2018

Crossrefs

Cf. A169888, A318431, A318432.

Column k=5 of A304482.

Sequence in context: A061964 A133667 A354848 * A205338 A197857 A197741

Adjacent sequences: A318430 A318431 A318432 * A318434 A318435 A318436

Keyword

nonn

Author

Marko Riedel, Aug 26 2018

Status

approved