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%I #7 Sep 02 2012 17:36:16
%S 1,1,2,8,44,411,4682,66524,1111134,21437357,469070942,11488238992,
%T 311505013052,9267596377239,300239975166840,10523614185609344,
%U 396861212733968144,16024522976922760209,689852631578947368422
%N Number of trees with n edges equipped with a cyclic order on their edges, i.e., number of orbits of the action of Z/nZ on the set of edge-labeled trees of size n, given by cyclically permuting the labels.
%F a(1) = 1, a(2) = 1, a(n) = (1/n)*((n+1)^{n-2} + sum_{k=1}^{n-1} (n+1)^{gcd(n,k)-1}) for n > 2
%o (Sage) [1,1] + [((n+1)^(n-2) + sum([(n+1)^(gcd(n,k) -1) for k in [1..n-1]]))/n for n in [3..20]]
%Y A007830, A000169
%K easy,nonn
%O 1,3
%A _Nikos Apostolakis_, Mar 10 2009
%E Corrected the formula and Sage code - Nikos Apostolakis, Feb 27 2011.
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