OFFSET
1,3
COMMENTS
A rooted partition of n is an integer partition of n - 1. A rooted twice-partition of n is a choice of a rooted partition of each part in a rooted partition of n.
EXAMPLE
The a(8) = 18 rooted twice-partitions where the composite rooted partition is strict:
(6), (51), (42), (321),
(5)(), (41)(), (32)(), (4)(1), (3)(2),
(4)()(), (31)()(), (3)(1)(),
(3)()()(), (21)()()(), (2)(1)()(),
(2)()()()(),
(1)()()()()(),
()()()()()()().
MATHEMATICA
twirtns[n_]:=Join@@Table[Tuples[IntegerPartitions[#-1]&/@ptn], {ptn, IntegerPartitions[n-1]}];
Table[Select[twirtns[n], UnsameQ@@Join@@#&]//Length, {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 26 2018
STATUS
approved