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%I #10 Sep 14 2018 02:48:58
%S 1,1,2,3,5,7,14,25,50,101,207,426,902,1917,4108,8887,19335,42330,
%T 93130,205894,456960,1018098,2275613,5102248,11471107,25856413
%N Number of locally stable rooted trees with n nodes, meaning no branch is a submultiset of any other (unequal) branch of the same root.
%H Gus Wiseman, <a href="/A316475/a316475.png">The a(8) = 25 locally stable rooted trees with 8 nodes.</a>
%e The a(6) = 7 locally stable rooted trees:
%e (((((o)))))
%e ((((oo))))
%e (((ooo)))
%e (((o)(o)))
%e ((oooo))
%e ((o)((o)))
%e (ooooo)
%t submultisetQ[M_,N_]:=Or[Length[M]==0,MatchQ[{Sort[List@@M],Sort[List@@N]},{{x_,Z___},{___,x_,W___}}/;submultisetQ[{Z},{W}]]]
%t strut[n_]:=strut[n]=If[n===1,{{}},Select[Join@@Function[c,Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1],Select[Tuples[#,2],UnsameQ@@#&&submultisetQ@@#&]=={}&]];
%t Table[Length[strut[n]],{n,15}]
%Y Cf. A000081, A285572, A285573, A303362, A304713, A316468, A316470, A316473, A316474.
%K nonn,more
%O 1,3
%A _Gus Wiseman_, Jul 04 2018
%E a(21)-a(26) from _Robert Price_, Sep 13 2018
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