A157994 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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