A317546 Number of multimin partitions of integer partitions of n.

1, 3, 7, 18, 42, 104, 246, 594, 1416, 3391, 8084, 19312, 46041, 109829, 261827, 624254, 1487981, 3546883, 8453770, 20149014, 48021864, 114451536, 272769936, 650084053, 1549312743

Offset: 1

Author

Gus Wiseman, Jul 31 2018

Keywords

• nonn

Comments

A multimin partition of m is an ordered multiset partition of m such that the minima of the blocks are weakly increasing.

Examples

			The a(3) = 7 multimin partitions of integer partitions of 3:
  (3),
  (1)(2), (12),
  (1)(1)(1), (1)(11), (11)(1), (111).
The a(4) = 18 multimin partitions of integer partitions of 4:
  (4),
  (1)(3), (13),
  (2)(2), (22),
  (1)(1)(2), (1)(12), (11)(2), (12)(1), (112),
  (1)(1)(1)(1), (1)(1)(11), (1)(11)(1), (1)(111), (11)(1)(1), (11)(11), (111)(1), (1111).
		

Crossrefs

Cf. A007716, A020639, A034691, A255397, A300335, A317545.

Programs

Mathematica

mmcount[m_List]:=mmcount[m]=If[Length[m]===0,0,1+Plus@@mmcount/@Union[Subsets[Rest[m]]]];
Table[Sum[mmcount[Reverse[ptn]],{ptn,IntegerPartitions[n]}],{n,25}]

Formula

a(n) = Sum_{k > 0 : A056239(k) = n} A317545(k).