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A301768 Number of ways to choose a strict rooted partition of each part in a constant rooted partition of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A239966 A304406 A053197 * A088145 A011754 A090105

Adjacent sequences:  A301765 A301766 A301767 * A301769 A301770 A301771

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 26 2018

STATUS

approved

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)