A309184 - OEIS

%I #11 Jul 18 2019 10:14:29

%S 1,4,31,244,2126,19780,192130,1922740,19692535,205444504,2175519380,

%T 23322657460,252631900236,2760767859784,30400169157656,

%U 336977765092788,3757141504436393,42107201575818028,474084628585822413,5359833704140818744,60823006052351729266

%N (1/5) times the number of n-member subsets of [5n] whose elements sum to a multiple of n.

%C Also (1/4) times the number of n-member subsets of [5n-1] whose elements sum to a multiple of n.

%H Alois P. Heinz, <a href="/A309184/b309184.txt">Table of n, a(n) for n = 1..925</a>

%F a(n) = 1/(5n) * Sum_{d|n} binomial(5d,d)*(-1)^(n+d)*phi(n/d).

%p with(numtheory):

%p a:= n-> add(binomial(5*d, d)*(-1)^(n+d)*

%p         phi(n/d), d in divisors(n))/(5*n):

%p seq(a(n), n=1..25);

%Y Column k=5 of A309148.

%K nonn

%O 1,2

%A _Alois P. Heinz_, Jul 15 2019