A323765 Dirichlet convolution of the integer partition numbers A000041 with the strict partition numbers A000009.

1, 1, 3, 5, 9, 10, 22, 20, 37, 44, 65, 68, 127, 119, 182, 226, 307, 335, 511, 544, 782, 913, 1171, 1359, 1908, 2121, 2738, 3286, 4174, 4821, 6305, 7182, 9108, 10739, 13195, 15548, 19465, 22397, 27477, 32423, 39448, 45843, 55995, 64871, 78343, 91761, 109325

Offset: 0

Author

Gus Wiseman, Jan 27 2019

Keywords

• nonn

Comments

Also the number of strict multiset partitions of constant multiset partitions of integer partitions of n.

Examples

			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))
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000009, A000041, A001970, A034729, A047968, A050343, A316980, A319066, A323764, A323766, A323774.

Programs

Mathematica

Join[{1}, Table[Sum[PartitionsQ[d]*PartitionsP[n/d],{d,Divisors[n]}],{n,1,100}]]

Formula

a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*n*sqrt(3)). - Vaclav Kotesovec, Jan 28 2019