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

1,3

Links

Table of n, a(n) for n=1..19.

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

Prog

(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]]

Crossrefs

A007830, A000169

Sequence in context: A336545 A126101 A308478 * A002500 A002833 A348107

Adjacent sequences: A157991 A157992 A157993 * A157995 A157996 A157997

Keyword

easy,nonn

Author

Nikos Apostolakis, Mar 10 2009

Extensions

Corrected the formula and Sage code - Nikos Apostolakis, Feb 27 2011.

Status

approved