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A301756
Number of ways to choose disjoint strict rooted partitions of each part in a strict rooted partition of n.
1
1, 1, 1, 2, 3, 5, 7, 10, 15, 22, 30, 42, 60, 85, 114, 155, 206, 286, 394, 524, 683, 910, 1187, 1564, 2090, 2751, 3543, 4606, 5917, 7598, 9771, 12651, 16260, 20822, 26421, 33525, 42463, 53594, 67337, 85299
OFFSET
1,4
COMMENTS
A rooted partition of n is an integer partition of n - 1.
EXAMPLE
The a(8) = 10 rooted twice-partitions:
(6), (51), (42), (321),
(5)(), (41)(), (32)(), (4)(1), (3)(2),
(3)(1)().
MATHEMATICA
twirtns[n_]:=Join@@Table[Tuples[IntegerPartitions[#-1]&/@ptn], {ptn, IntegerPartitions[n-1]}];
Table[Select[twirtns[n], And[UnsameQ@@Total/@#, UnsameQ@@Join@@#]&]//Length, {n, 20}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 26 2018
STATUS
approved