OFFSET
1,3
COMMENTS
A rooted partition of n is an integer partition of n - 1.
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 26 2018
STATUS
approved