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A323765
Dirichlet convolution of the integer partition numbers A000041 with the strict partition numbers A000009.
2
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
0,3
COMMENTS
Also the number of strict multiset partitions of constant multiset partitions of integer partitions of n.
LINKS
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}]]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 27 2019
STATUS
approved