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 A301345 #5 Mar 19 2018 22:06:31
%S A301345 1,1,0,0,1,0,0,1,1,0,0,0,2,1,0,0,0,1,3,1,0,0,0,1,2,4,1,0,0,0,0,3,4,5,
%T A301345 1,0,0,0,0,2,6,6,6,1,0,0,0,0,1,6,10,9,7,1,0,0,0,0,1,5,12,16,12,8,1,0,
%U A301345 0,0,0,0,4,13,22,23,16,9,1,0,0,0,0,0,3,14,27,36,32,20,10,1,0,0,0,0,0,2,11
%N A301345 Regular triangle where T(n,k) is the number of transitive rooted trees with n nodes and k leaves.
%e A301345 Triangle begins:
%e A301345 1
%e A301345 1 0
%e A301345 0 1 0
%e A301345 0 1 1 0
%e A301345 0 0 2 1 0
%e A301345 0 0 1 3 1 0
%e A301345 0 0 1 2 4 1 0
%e A301345 0 0 0 3 4 5 1 0
%e A301345 0 0 0 2 6 6 6 1 0
%e A301345 0 0 0 1 6 10 9 7 1 0
%e A301345 0 0 0 1 5 12 16 12 8 1 0
%e A301345 The T(9,5) = 6 transitive rooted trees: (o(o)(oo(o))), (o((oo))(oo)), (oo(o)(o(o))), (o(o)(o)(oo)), (ooo(o)((o))), (oo(o)(o)(o)).
%t A301345 rut[n_]:=rut[n]=If[n===1,{{}},Join@@Function[c,Union[Sort/@Tuples[rut/@c]]]/@IntegerPartitions[n-1]];
%t A301345 trat[n_]:=Select[rut[n],Complement[Union@@#,#]==={}&];
%t A301345 Table[Length[Select[trat[n],Count[#,{},{-2}]===k&]],{n,15},{k,n}]
%Y A301345 Row sums are A290689.
%Y A301345 Cf. A000081, A001190, A003238, A004111, A032305, A055277, A276625, A279861, A290760, A290822, A298422, A298426, A301342, A301343, A301344.
%K A301345 nonn,tabl
%O A301345 1,13
%A A301345 _Gus Wiseman_, Mar 19 2018