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

1,4

Comments

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

Links

Table of n, a(n) for n=1..40.

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}]

Crossrefs

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

Sequence in context: A184641 A225490 A076972 * A170877 A003410 A362757

Adjacent sequences: A301753 A301754 A301755 * A301757 A301758 A301759

Keyword

nonn,more

Author

Gus Wiseman, Mar 26 2018

Status

approved