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%I #6 Sep 16 2021 02:43:39
%S 1,2,3,5,6,11,13,21,28,38,51,73,93,124,163,212,278,352,459,572,736,
%T 914,1187,1434,1838
%N Number of partitions of n which occur as the automorphism orbit sizes of a rooted forest of n vertices.
%C Also, the number of partitions of n+1 which occur as the automorphism orbit sizes of a rooted tree of n+1 vertices, since the tree root is alone in its orbit and a tree without its root is a forest.
%H Kevin Ryde, <a href="/A347414/a347414.c.txt">C program using Nauty to calculate terms</a>
%e For n=9, one of the partitions counted is 1+1+1+2+2+2 = 9 which is the orbit sizes of the following forest (and various other forests too):
%e roots: a c orbit: a b c d e f
%e | / \ size: 1 1 1 2 2 2
%e children: b e e
%e / \ | |
%e d d f f
%Y Cf. A337114 (in free trees), A000041 (all partitions).
%K nonn,more
%O 1,2
%A _Kevin Ryde_, Aug 31 2021
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