A301763 Number of ways to choose a constant rooted partition of each part in a constant rooted partition of n.

1, 1, 2, 3, 4, 4, 8, 5, 8, 13, 14, 5, 32, 7, 20, 64, 26, 6, 92, 7, 126, 199, 22, 5, 352, 252, 41, 581, 394, 7, 1832, 9, 292, 2119, 31, 3216, 4946, 10, 40, 8413, 7708, 9, 20656, 9, 2324, 53546, 24, 5, 70040, 16395, 59361, 131204, 9503, 7, 266780, 178180, 82086

Offset

1,3

Comments

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

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Example

The a(7) = 8 rooted twice-partitions: (5), (11111), (2)(2), (2)(11), (11)(2), (11)(11), (1)(1)(1), ()()()()()().
The a(15) = 20 rooted twice-partitions:
()()()()()()()()()()()()()(),
(1)(1)(1)(1)(1)(1)(1), (111111)(111111), (1111111111111),
(111111)(222), (222)(111111), (222)(222),
(111111)(33), (222)(33), (33)(111111), (33)(222), (33)(33),
(111111)(6), (222)(6), (33)(6), (6)(111111), (6)(222), (6)(33), (6)(6),
(13).

Mathematica

Table[If[n===1, 1, Sum[If[d===n-1, 1, DivisorSigma[0, (n-1)/d-1]]^d, {d, Divisors[n-1]}]], {n, 50}]

Prog

(PARI) a(n)=if(n==1, 1, sumdiv(n-1, d, if(d==n-1, 1, numdiv((n-1)/d-1)^d))) \\ Andrew Howroyd, Aug 26 2018

Crossrefs

Cf. A000005, A002865, A047968, A063834, A093637, A127524, A295924, A300383, A301422, A301462, A301467, A301480, A301706.

Sequence in context: A241315 A136330 A294267 * A236129 A240219 A028298

Adjacent sequences: A301760 A301761 A301762 * A301764 A301765 A301766

Keyword

nonn

Author

Gus Wiseman, Mar 26 2018

Status

approved