cp's OEIS Frontend

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

%I A316772 #8 Sep 15 2018 02:04:59
%S A316772 1,1,2,4,11,27,75,202,565,1602,4617,13472,39781,118604,356605,1080178,
%T A316772 3293109,10097356,31118507,96341035
%N A316772 Number of series-reduced locally nonintersecting rooted trees whose leaves form an integer partition of n.
%C A316772 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.
%e A316772 The a(6) = 27 trees:
%e A316772 6,
%e A316772 (15),
%e A316772 (24),
%e A316772 (1(14)), (114),
%e A316772 (1(23)), (2(13)), (3(12)), (123),
%e A316772 (1(1(13))), (1(113)), (11(13)), (1113),
%e A316772 (1(2(12))), (1(122)), (2(1(12))), (2(112)), (12(12)), (1122),
%e A316772 (1(1(1(12)))), (1(1(112))), (1(11(12))), (1(1112)), (11(1(12))), (11(112)), (111(12)), (11112).
%t A316772 nms[n_]:=nms[n]=Prepend[Join@@Table[Select[Union[Sort/@Tuples[nms/@ptn]],Intersection@@#=={}&],{ptn,Rest[IntegerPartitions[n]]}],{n}];
%t A316772 Table[Length[nms[n]],{n,10}]
%Y A316772 Cf. A000081, A000669, A001678, A141268, A292504, A316500, A316501, A316503, A316651, A316652, A316655.
%K A316772 nonn,more
%O A316772 1,3
%A A316772 _Gus Wiseman_, Jul 12 2018
%E A316772 a(17)-a(20) from _Robert Price_, Sep 14 2018