A157994 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.
1, 1, 2, 8, 44, 411, 4682, 66524, 1111134, 21437357, 469070942, 11488238992, 311505013052, 9267596377239, 300239975166840, 10523614185609344, 396861212733968144, 16024522976922760209, 689852631578947368422
Offset: 1
Programs
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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]]
Formula
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
Extensions
Corrected the formula and Sage code - Nikos Apostolakis, Feb 27 2011.