A319291 Number of series-reduced locally disjoint rooted trees with n leaves spanning an initial interval of positive integers.

1, 2, 12, 107, 1299, 20764, 412957, 9817743

Offset

1,2

Links

Table of n, a(n) for n=1..8.

Example

The a(3) = 12 series-reduced locally disjoint rooted trees:
  (1(11))
   (111)
  (1(22))
  (2(12))
   (122)
  (1(12))
  (2(11))
   (112)
  (1(23))
  (2(13))
  (3(12))
   (123)
The trees counted by A316651(4) but not by a(4):
  ((11)(12))
  ((12)(13))
  ((12)(22))
  ((12)(23))
  ((13)(23))

Mathematica

disjointQ[u_]:=Apply[And, Outer[#1==#2||Intersection[#1, #2]=={}&, u, u, 1], {0, 1}];
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
gro[m_]:=gro[m]=If[Length[m]==1, {m}, Select[Union[Sort/@Join@@(Tuples[gro/@#]&/@Select[mps[m], Length[#]>1&])], disjointQ]];
allnorm[n_Integer]:=Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1];
Table[Sum[Length[gro[m]], {m, allnorm[n]}], {n, 5}]

Crossrefs

Cf. A000081, A007562, A301700, A316473, A316475, A316495, A316651, A316694, A316695, A316696, A316697, A319286.

Sequence in context: A275765 A184975 A268538 * A265132 A080446 A301411

Adjacent sequences: A319288 A319289 A319290 * A319292 A319293 A319294

Keyword

nonn,more

Author

Gus Wiseman, Sep 16 2018

Status

approved