This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A316473 #11 Jun 20 2020 03:20:28
%S A316473 1,1,2,4,9,19,44,99,233,554,1346,3300,8219,20635,52300,133488,343033,
%T A316473 886360,2302133,6005835
%N A316473 Number of locally disjoint rooted trees with n nodes, meaning no branch overlaps any other (unequal) branch of the same root.
%H A316473 Gus Wiseman, <a href="/A316473/a316473.png">The a(6) = 19 locally disjoint rooted trees.</a>
%e A316473 The a(5) = 9 locally disjoint rooted trees:
%e A316473 ((((o))))
%e A316473 (((oo)))
%e A316473 ((o(o)))
%e A316473 ((ooo))
%e A316473 (o((o)))
%e A316473 (o(oo))
%e A316473 ((o)(o))
%e A316473 (oo(o))
%e A316473 (oooo)
%t A316473 strut[n_]:=strut[n]=If[n===1,{{}},Select[Join@@Function[c,Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1],Select[Tuples[#,2],UnsameQ@@#&&(Intersection@@#=!={})&]=={}&]];
%t A316473 Table[Length[strut[n]],{n,15}]
%Y A316473 Cf. A000081, A285573, A302696, A304713, A316468, A316470, A316471, A316475, A316495.
%K A316473 nonn,more
%O A316473 1,3
%A A316473 _Gus Wiseman_, Jul 04 2018
%E A316473 a(20) from _Jinyuan Wang_, Jun 20 2020