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A124776
Number of labeled partially ordered sets associated with compositions in standard order.
2
1, 1, 1, 2, 1, 9, 3, 6, 1, 28, 54, 60, 4, 36, 12, 24
OFFSET
0,4
COMMENTS
The standard order of compositions is given by A066099.
The k-th term of the composition is the number of objects with rank k. The rank of an object is one more than the maximum rank of any smaller object in the ordering (1 for a minimal element), or equivalently the size of the largest chain of which the object is the maximal element.
EXAMPLE
Composition number 11 is 2,1,1; there are 3 partial orders
associated with this (shown below); these can be labeled respectively
in 12, 24 and 24 ways, so a(11) = 12+24+24 = 60.
..O..*O..*..O
..|..*|..*./|
..O..*O..*O.|
./.\.*|..*|.|
O...O*O.O*O.O
The table starts:
1
1
1 2
1 9 3 6
CROSSREFS
Cf. A066099, A124775, A124777, A011782 (row lengths), A001035 (row sums).
Sequence in context: A095888 A160510 A298738 * A099285 A249264 A188108
KEYWORD
more,nonn,tabf
AUTHOR
STATUS
approved