OFFSET
1,4
COMMENTS
A subset of totally transitive rooted trees (A318185).
EXAMPLE
The a(1) = 1 through a(8) = 8 rooted trees:
o (o) (oo) (ooo) (oooo) (ooooo) (oooooo) (ooooooo)
(o(o)) (oo(o)) (oo(oo)) (ooo(oo)) (ooo(ooo))
(ooo(o)) (oooo(o)) (oooo(oo))
(o(o)(o)) (oo(o)(o)) (ooooo(o))
(oo(o)(oo))
(ooo(o)(o))
(o(o)(o)(o))
(o(o)(o(o)))
MATHEMATICA
submultQ[cap_, fat_]:=And@@Function[i, Count[fat, i]>=Count[cap, i]]/@Union[List@@cap];
rallt[n_]:=Select[Union[Sort/@Join@@(Tuples[rallt/@#]&/@IntegerPartitions[n-1])], And@@Table[submultQ[b, #], {b, #}]&];
Table[Length[rallt[n]], {n, 10}]
CROSSREFS
The Matula-Goebel numbers of these trees are given by A324842.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 18 2019
STATUS
approved