%I #15 Sep 11 2018 05:01:40

%S 1,1,2,4,9,20,51,128,345,940,2632,7450,21434,62174,182146,537369,

%T 1596133,4767379,14312919,43162856,130695821,397184252,1211057426,

%U 3703794849,11358759346,34923477315,107627138308,332404636811

%N Number of rooted compound windmills (mobiles) of n nodes.

%C Also the number of locally necklace plane trees with n nodes, where a plane tree is locally necklace if the sequence of branches directly under any given node is lexicographically minimal among its cyclic permutations. - _Gus Wiseman_, Sep 05 2018

%D F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 241 (3.3.84).

%H Andrew Howroyd, <a href="/A032200/b032200.txt">Table of n, a(n) for n = 1..200</a>

%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>

%H <a href="/index/Mo#mobiles">Index entries for sequences related to mobiles</a>

%F Shifts left under "CIK" (necklace, indistinct, unlabeled) transform.

%e From _Gus Wiseman_, Sep 05 2018: (Start)

%e The a(5) = 9 locally necklace plane trees:

%e ((((o))))

%e (((oo)))

%e ((o(o)))

%e (o((o)))

%e ((o)(o))

%e ((ooo))

%e (o(oo))

%e (oo(o))

%e (oooo)

%e (End)

%t neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];

%t neckplane[n_]:=If[n==1,{{}},Join@@Table[Select[Tuples[neckplane/@c],neckQ],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];

%t Table[Length[neckplane[n]],{n,10}] (* _Gus Wiseman_, Sep 05 2018 *)

%o (PARI)

%o CIK(p,n)={sum(d=1, n, eulerphi(d)/d*log(subst(1/(1+O(x*x^(n\d))-p), x, x^d)))}

%o seq(n)={my(p=O(1));for(i=1, n, p=1+CIK(x*p, i)); Vec(p)} \\ _Andrew Howroyd_, Jun 20 2018

%Y Cf. A029768, A038037, A055340.

%Y Cf. A000108, A007853, A032171, A254040, A304173, A304175, A317852.

%K nonn,eigen

%O 1,3

%A _Christian G. Bower_