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 A324838 #5 Mar 19 2019 07:14:30
%S A324838 1,0,1,2,5,10,28,64,169,422,1108,2872,7627,20202,54216,145867,395288
%N A324838 Number of unlabeled rooted trees with n nodes where the branches of no branch of the root form a submultiset of the branches of the root.
%e A324838 The a(1) = 1 through a(6) = 10 rooted trees:
%e A324838 o ((o)) ((oo)) ((ooo)) ((oooo))
%e A324838 (((o))) (((oo))) (((ooo)))
%e A324838 ((o)(o)) ((o)(oo))
%e A324838 ((o(o))) ((o(oo)))
%e A324838 ((((o)))) ((oo(o)))
%e A324838 ((((oo))))
%e A324838 (((o)(o)))
%e A324838 (((o(o))))
%e A324838 ((o((o))))
%e A324838 (((((o)))))
%t A324838 submultQ[cap_,fat_]:=And@@Function[i,Count[fat,i]>=Count[cap,i]]/@Union[List@@cap];
%t A324838 rtall[n_]:=Union[Sort/@Join@@(Tuples[rtall/@#]&/@IntegerPartitions[n-1])];
%t A324838 Table[Length[Select[rtall[n],And@@Table[!submultQ[b,#],{b,#}]&]],{n,10}]
%Y A324838 Cf. A000081, A290689, A304360, A306844, A317787, A318185.
%Y A324838 Cf. A324694, A324696, A324704, A324738, A324744, A324758, A324759, A324765, A324768, A324771, A324839, A324840, A324844, A324846.
%K A324838 nonn,more
%O A324838 1,4
%A A324838 _Gus Wiseman_, Mar 18 2019