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 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 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=1..25. FORMULA a(n) = Sum_{k > 0 : A056239(k) = n} A317545(k). 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 Cf. A007716, A020639, A034691, A255397, A300335, A317545. Sequence in context: A036884 A102291 A034691 * A319001 A036669 A000633 Adjacent sequences: A317543 A317544 A317545 * A317547 A317548 A317549 KEYWORD nonn AUTHOR Gus Wiseman, Jul 31 2018 STATUS approved

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