A316772 Number of series-reduced locally nonintersecting rooted trees whose leaves form an integer partition of n.

1, 1, 2, 4, 11, 27, 75, 202, 565, 1602, 4617, 13472, 39781, 118604, 356605, 1080178, 3293109, 10097356, 31118507, 96341035

Offset: 1

Author

Gus Wiseman, Jul 12 2018

Keywords

• nonn
• more

Comments

A rooted tree is series-reduced if all non-leaf nodes have at least two branches. It is locally nonintersecting if the intersection of all branches directly under any given root is empty.

Examples

			The a(6) = 27 trees:
6,
(15),
(24),
(1(14)), (114),
(1(23)), (2(13)), (3(12)), (123),
(1(1(13))), (1(113)), (11(13)), (1113),
(1(2(12))), (1(122)), (2(1(12))), (2(112)), (12(12)), (1122),
(1(1(1(12)))), (1(1(112))), (1(11(12))), (1(1112)), (11(1(12))), (11(112)), (111(12)), (11112).
		

Crossrefs

Cf. A000081, A000669, A001678, A141268, A292504, A316500, A316501, A316503, A316651, A316652, A316655.

Programs

Mathematica

nms[n_]:=nms[n]=Prepend[Join@@Table[Select[Union[Sort/@Tuples[nms/@ptn]],Intersection@@#=={}&],{ptn,Rest[IntegerPartitions[n]]}],{n}];
Table[Length[nms[n]],{n,10}]

Extensions

a(17)-a(20) from Robert Price, Sep 14 2018