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A309184 (1/5) times the number of n-member subsets of [5n] whose elements sum to a multiple of n.

%I A309184 #11 Jul 18 2019 10:14:29
%S A309184 1,4,31,244,2126,19780,192130,1922740,19692535,205444504,2175519380,
%T A309184 23322657460,252631900236,2760767859784,30400169157656,
%U A309184 336977765092788,3757141504436393,42107201575818028,474084628585822413,5359833704140818744,60823006052351729266
%N A309184 (1/5) times the number of n-member subsets of [5n] whose elements sum to a multiple of n.
%C A309184 Also (1/4) times the number of n-member subsets of [5n-1] whose elements sum to a multiple of n.
%H A309184 Alois P. Heinz, <a href="/A309184/b309184.txt">Table of n, a(n) for n = 1..925</a>
%F A309184 a(n) = 1/(5n) * Sum_{d|n} binomial(5d,d)*(-1)^(n+d)*phi(n/d).
%p A309184 with(numtheory):
%p A309184 a:= n-> add(binomial(5*d, d)*(-1)^(n+d)*
%p A309184         phi(n/d), d in divisors(n))/(5*n):
%p A309184 seq(a(n), n=1..25);
%Y A309184 Column k=5 of A309148.
%K A309184 nonn
%O A309184 1,2
%A A309184 _Alois P. Heinz_, Jul 15 2019