A301762 Number of ways to choose a constant rooted partition of each part in a rooted partition of n.

1, 1, 2, 4, 7, 12, 21, 34, 55, 90, 143, 220, 347, 528, 805, 1226, 1831, 2719, 4048, 5940, 8710, 12714, 18403, 26529, 38220, 54679, 77899, 110810, 156848, 221181, 311635, 436705, 610597, 852125, 1184928, 1644136, 2276551, 3142523, 4328960, 5953523, 8167209

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..41.

Formula

O.g.f.: Product_{n>0} 1/(1 - d(n-1) x^n) where d(n) = A000005(n) and d(0) = 1.

Example

The a(5) = 7 rooted twice-partitions where the latter rooted partitions are constant: (3), (111), (2)(), (11)(), (1)(1), (1)()(), ()()()().

Mathematica

Table[Sum[Product[If[k===1, 1, DivisorSigma[0, k-1]], {k, ptn}], {ptn, IntegerPartitions[n-1]}], {n, 20}]

Crossrefs

Cf. A002865, A063834, A093637, A279784, A295935, A300383, A301422, A301462, A301467, A301480, A301706.

Sequence in context: A305106 A182746 A100482 * A003293 A192759 A289249

Adjacent sequences: A301759 A301760 A301761 * A301763 A301764 A301765

Keyword

nonn

Author

Gus Wiseman, Mar 26 2018

Status

approved