A323764 Dirichlet self-convolution of the integer partition numbers A000041.

1, 1, 4, 6, 14, 14, 34, 30, 64, 69, 112, 112, 228, 202, 330, 394, 575, 594, 956, 980, 1492, 1674, 2228, 2510, 3700, 3965, 5276, 6200, 8126, 9130, 12318, 13684, 17842, 20622, 25808, 29976, 38377, 43274, 53990, 62976, 77912, 89166, 110656, 126522, 154918, 179744

Offset: 0

Author

Gus Wiseman, Jan 27 2019

Keywords

• nonn

Comments

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

Examples

			The a(4) = 14 multiset partitions of constant multiset partitions:
  ((1111))              ((22))      ((4))  ((31))  ((211))
  ((11)(11))            ((2)(2))
  ((11))((11))          ((2))((2))
  ((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. A000041, A000837, A001970, A002033, A003238, A034729, A047968, A279787, A305551, A306017, A319056, A323774.

Programs

Mathematica

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

Formula

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