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A157994
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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.
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0
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1, 1, 2, 8, 44, 411, 4682, 66524, 1111134, 21437357, 469070942, 11488238992, 311505013052, 9267596377239, 300239975166840, 10523614185609344, 396861212733968144, 16024522976922760209, 689852631578947368422
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OFFSET
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1,3
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LINKS
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Table of n, a(n) for n=1..19.
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FORMULA
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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
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PROG
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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]]
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CROSSREFS
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A007830, A000169
Sequence in context: A336545 A126101 A308478 * A002500 A002833 A139015
Adjacent sequences: A157991 A157992 A157993 * A157995 A157996 A157997
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KEYWORD
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easy,nonn
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AUTHOR
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Nikos Apostolakis, Mar 10 2009
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EXTENSIONS
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Corrected the formula and Sage code - Nikos Apostolakis, Feb 27 2011.
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STATUS
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approved
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