A301756 Number of ways to choose disjoint strict rooted partitions of each part in a strict rooted partition of n.

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

Author

Gus Wiseman, Mar 26 2018

Keywords

• nonn
• more

Comments

A rooted partition of n is an integer partition of n - 1.

Examples

			The a(8) = 10 rooted twice-partitions:
(6), (51), (42), (321),
(5)(), (41)(), (32)(), (4)(1), (3)(2),
(3)(1)().
		

Crossrefs

Cf. A002865, A032305, A063834, A093637, A275780, A279375, A294786, A301422, A301462, A301467, A301480, A301706.

Programs

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}]