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

Author

Gus Wiseman, Mar 26 2018

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

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

Programs

Mathematica

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