A319123 Number of series-reduced plane trees with n leaves such that each branch directly under any given node has a different number of leaves.

1, 1, 3, 7, 21, 75, 277, 1083, 4419, 18493, 77729, 332557, 1444477, 6307225, 27912147, 123878207, 554733045, 2492087531, 11280537097, 51120499279, 233319480419, 1065835004917, 4895443823281, 22505853359485, 103958158302085, 480365303903637, 2229412587062123

Offset

1,3

Links

Table of n, a(n) for n=1..27.

Example

The a(4) = 7 plane trees:
  (oooo)
  (o(ooo))
  ((ooo)o)
  (o(o(oo)))
  (o((oo)o))
  ((o(oo))o)
  (((oo)o)o)

Mathematica

b[n_]:=b[n]=1+Sum[Times@@b/@f, {f, Join@@Permutations/@Select[IntegerPartitions[n], And[Length[#]>1, UnsameQ@@#]&]}];
Array[b, 30]

Crossrefs

Cf. A000108, A001003, A007853, A074206, A118376, A273873, A277130, A281113, A304173, A304175, A319122.

Sequence in context: A169587 A075211 A075212 * A173794 A049365 A288849

Adjacent sequences: A319120 A319121 A319122 * A319124 A319125 A319126

Keyword

nonn

Author

Gus Wiseman, Sep 11 2018

Status

approved