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

Author

Gus Wiseman, Sep 11 2018

Keywords

• nonn

Examples

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

Crossrefs

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

Programs

Mathematica

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