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

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, A318432.

Column k=5 of A304482.

Programs

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)));

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

Formula

a(n) = (-1)^n * (1/n) * Sum_{d|n} C(5d,d)*(-1)^d*phi(n/d) for n>0, a(0)=1.