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%I #6 Jul 31 2018 07:23:58
%S 1,3,7,18,42,104,246,594,1416,3391,8084,19312,46041,109829,261827,
%T 624254,1487981,3546883,8453770,20149014,48021864,114451536,272769936,
%U 650084053,1549312743
%N Number of multimin partitions of integer partitions of n.
%C A multimin partition of m is an ordered multiset partition of m such that the minima of the blocks are weakly increasing.
%F a(n) = Sum_{k > 0 : A056239(k) = n} A317545(k).
%e The a(3) = 7 multimin partitions of integer partitions of 3:
%e (3),
%e (1)(2), (12),
%e (1)(1)(1), (1)(11), (11)(1), (111).
%e The a(4) = 18 multimin partitions of integer partitions of 4:
%e (4),
%e (1)(3), (13),
%e (2)(2), (22),
%e (1)(1)(2), (1)(12), (11)(2), (12)(1), (112),
%e (1)(1)(1)(1), (1)(1)(11), (1)(11)(1), (1)(111), (11)(1)(1), (11)(11), (111)(1), (1111).
%t mmcount[m_List]:=mmcount[m]=If[Length[m]===0,0,1+Plus@@mmcount/@Union[Subsets[Rest[m]]]];
%t Table[Sum[mmcount[Reverse[ptn]],{ptn,IntegerPartitions[n]}],{n,25}]
%Y Cf. A007716, A020639, A034691, A255397, A300335, A317545.
%K nonn
%O 1,2
%A _Gus Wiseman_, Jul 31 2018
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