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From Gus Wiseman, Oct 27 2022: (Start)
The a(3) = 1 through a(9) = 16 partitions:
(321) (431) (532) (642) (743) (853) (954)
(541) (651) (752) (862) (963)
(4321) (5421) (761) (871) (972)
(6321) (5432) (6532) (981)
(6431) (7531) (6543)
(6521) (7621) (7542)
(7421) (8431) (7632)
(8521) (8541)
(64321) (8631)
(8721)
(9432)
(9531)
(9621)
(65421)
(75321)
(84321)
(End)
From Gus Wiseman, Oct 27 2022: (Start)
The a(3) = 1 through a(9) = 16 partitions:
(321) (431) (532) (642) (743) (853) (954)
(541) (651) (752) (862) (963)
(4321) (5421) (761) (871) (972)
(6321) (5432) (6532) (981)
(6431) (7531) (6543)
(6521) (7621) (7542)
(7421) (8431) (7632)
(8521) (8541)
(64321) (8631)
(8721)
(9432)
(9531)
(9621)
(65421)
(75321)
(84321)
(End)
The non-strict version is A002219, ranked by A357976.
These partitions are ranked by A357854.
A000712 counts distinct submultisets of partitions, strict A032302.
A027187 counts partitions of even length.
A056239 adds up prime indices, row sums of A112798.
A304792 counts subset-sums of partitions, positive A276024, strict A284640.
Cf. A006827, A063834, A064914, A108917, `A122768, A235130, A237194, A276107, A300061, `~A304793, ~`A321144, A357879.
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Fausto A. C. Cariboni, <a href="/A237258/b237258.txt">Table of n, a(n) for n = 0..200</a>
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