OFFSET
0,3
COMMENTS
Also the number of strict multiset partitions of constant multiset partitions of integer partitions of n.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
FORMULA
a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*n*sqrt(3)). - Vaclav Kotesovec, Jan 28 2019
EXAMPLE
The a(1) = 1 through a(5) = 10 strict multiset partitions of constant multiset partitions of integer partitions:
((1)) ((2)) ((3)) ((4)) ((5))
((11)) ((21)) ((31)) ((41))
((1)(1)) ((111)) ((22)) ((32))
((1)(1)(1)) ((211)) ((311))
((1))((1)(1)) ((1111)) ((221))
((2)(2)) ((2111))
((11)(11)) ((11111))
((1)(1)(1)(1)) ((1)(1)(1)(1)(1))
((1))((1)(1)(1)) ((1))((1)(1)(1)(1))
((1)(1))((1)(1)(1))
MATHEMATICA
Join[{1}, Table[Sum[PartitionsQ[d]*PartitionsP[n/d], {d, Divisors[n]}], {n, 1, 100}]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 27 2019
STATUS
approved