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 A331684 #6 Feb 01 2020 07:09:30
%S A331684 1,1,2,3,6,14,30,68,157,379,901,2229,5488,13846,34801,89368,228186,
%T A331684 592943,1533511,4026833
%N A331684 Number of locally disjoint enriched identity p-trees of weight n.
%C A331684 A locally disjoint enriched identity p-tree of weight n is either the number n itself or a finite sequence of distinct non-overlapping locally disjoint enriched identity p-trees whose weights are weakly decreasing and sum to n.
%e A331684 The a(1) = 1 through a(6) = 14 enriched p-trees:
%e A331684 1 2 3 4 5 6
%e A331684 (21) (31) (32) (42)
%e A331684 ((21)1) (41) (51)
%e A331684 ((21)2) (321)
%e A331684 ((31)1) ((21)3)
%e A331684 (((21)1)1) ((31)2)
%e A331684 ((32)1)
%e A331684 (3(21))
%e A331684 ((41)1)
%e A331684 ((21)21)
%e A331684 (((21)1)2)
%e A331684 (((21)2)1)
%e A331684 (((31)1)1)
%e A331684 ((((21)1)1)1)
%t A331684 disjointQ[u_]:=Apply[And,Outer[#1==#2||Intersection[#1,#2]=={}&,u,u,1],{0,1}];
%t A331684 ldeip[n_]:=Prepend[Select[Join@@Table[Tuples[ldeip/@p],{p,Rest[IntegerPartitions[n]]}],UnsameQ@@#&&disjointQ[DeleteCases[#,_Integer]]&],n];
%t A331684 Table[Length[ldeip[n]],{n,12}]
%Y A331684 The orderless version is A316694.
%Y A331684 The non-identity version is A331687.
%Y A331684 Identity trees are A004111.
%Y A331684 P-trees are A196545.
%Y A331684 Enriched p-trees are A289501.
%Y A331684 Locally disjoint identity trees are A316471.
%Y A331684 Enriched identity p-trees are A331875, with locally disjoint case A331687.
%Y A331684 Cf. A000669, A005804, A141268, A300660, A316696, A316697, A331678, A331679, A331680, A331683, A331686, A331783, A331874.
%K A331684 nonn,more
%O A331684 1,3
%A A331684 _Gus Wiseman_, Jan 31 2020