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%I #18 Aug 28 2018 19:27:25
%S 1,5,20,155,1220,10630,98900,960650,9613700,98462675,1027222520,
%T 10877596900,116613287300,1263159501180,13803839298920,
%U 152000845788280,1684888825463940,18785707522181965,210536007879090140,2370423142929112065,26799168520704093720
%N Number of n-element subsets of [5n] whose elements sum to a multiple of n.
%H Marko Riedel et al., <a href="https://math.stackexchange.com/questions/2894653/">Number of n-element subsets divisible by n</a>
%F a(n) = (-1)^n * (1/n) * Sum_{d|n} C(5d,d)*(-1)^d*phi(n/d) for n>0, a(0)=1.
%p 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)));
%o (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
%Y Cf. A169888, A318431, A318432.
%Y Column k=5 of A304482.
%K nonn
%O 0,2
%A _Marko Riedel_, Aug 26 2018
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