A301768 Number of ways to choose a strict rooted partition of each part in a constant rooted partition of n.

1, 1, 2, 2, 4, 3, 6, 5, 11, 8, 14, 11, 32, 16, 36, 32, 70, 33, 104, 47, 168, 130, 178, 90, 521, 155, 369, 383, 902, 223, 1562, 297, 1952, 1392, 1474, 1665, 6297, 669, 2878, 4241, 12401, 1114, 17474, 1427, 19436, 20754, 9971, 2305, 80110, 19295, 51942, 36428

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..52.

Example

The a(9) = 11 rooted twice-partitions:
(7), (61), (52), (43), (421),
(3)(3), (3)(21), (21)(3), (21)(21),
(1)(1)(1)(1),
()()()()()()()().

Mathematica

Table[Sum[PartitionsQ[n/d-1]^d, {d, Divisors[n]}], {n, 50}]

Crossrefs

Cf. A002865, A063834, A093637, A127524, A279788, A296132, A301422, A301462, A301467, A301480, A301706.

Sequence in context: A304406 A053197 A275234 * A088145 A011754 A090105

Adjacent sequences: A301765 A301766 A301767 * A301769 A301770 A301771

Keyword

nonn

Author

Gus Wiseman, Mar 26 2018

Status

approved