OFFSET
0,3
COMMENTS
An unlabeled version of A279789.
FORMULA
a(0) = 1; a(n) = Sum_{d|n} binomial(tau(d) + n/d - 1, n/d), where tau = A000005.
EXAMPLE
The a(1) = 1 through a(6) = 12 multiset partitions:
(1) (2) (3) (4) (5) (6)
(11) (111) (22) (11111) (33)
(1)(1) (1)(1)(1) (1111) (1)(1)(1)(1)(1) (222)
(2)(2) (3)(3)
(2)(11) (111111)
(11)(11) (3)(111)
(1)(1)(1)(1) (2)(2)(2)
(111)(111)
(2)(2)(11)
(2)(11)(11)
(11)(11)(11)
(1)(1)(1)(1)(1)(1)
MATHEMATICA
Table[Length[Join@@Table[Union[Sort/@Tuples[Select[IntegerPartitions[#], SameQ@@#&]&/@ptn]], {ptn, Select[IntegerPartitions[n], SameQ@@#&]}]], {n, 30}]
PROG
(PARI) a(n) = if (n==0, 1, sumdiv(n, d, binomial(numdiv(d) + n/d - 1, n/d))); \\ Michel Marcus, Jan 28 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 27 2019
STATUS
approved