

A317546


Number of multimin partitions of integer partitions of n.


14



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
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OFFSET

1,2


COMMENTS

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


LINKS



FORMULA



EXAMPLE

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).


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}]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



