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
FORMULA
a(n) = Sum_{d | n-1} A000041((n-1)/d-1)^d for n > 1. - Andrew Howroyd, Aug 26 2018
EXAMPLE
The a(7) = 13 rooted twice-partitions:
(5), (41), (32), (311), (221), (2111), (11111),
(2)(2), (2)(11), (11)(2), (11)(11),
(1)(1)(1),
()()()()()().
MATHEMATICA
Table[Sum[PartitionsP[n/d-1]^d, {d, Divisors[n]}], {n, 50}]
PROG
(PARI) a(n)=if(n==1, 1, sumdiv(n-1, d, numbpart((n-1)/d-1)^d)) \\ Andrew Howroyd, Aug 26 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 26 2018
STATUS
approved