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A125311
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Array giving number of (k,2)-noncrossing partitions of n, read by antidiagonals.
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3
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1, 1, 1, 1, 1, 2, 1, 1, 2, 5, 1, 1, 2, 5, 14, 1, 1, 2, 5, 15, 42, 1, 1, 2, 5, 15, 51, 132, 1, 1, 2, 5, 15, 52, 188, 429
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| A partition of [n]={1,2,...,n} is a collection B_1 union ... union B_{d} of nonempty disjoint subsets of [n] such that B = union B_{d}=[n]. Any partition can be expressed by its canonical sequential form pi_1,pi_2...pi_{n}, where pi_{i}=j is the element i in the block B_{j}. In this paper, we find an explicit formula of the ordinary generating function for the number of (k,d)-noncrossing partitions of [n] for d=1,2, namely the number of partitions of [n] with canonical sequential form avoiding either 12...k1 or 12...k12.
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REFERENCES
| Toufik Mansour and Simone Severini, Enumeration of (k,2)-noncrossing partitions, Discrete Math., 308 (2008), 4570-4577.
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LINKS
| Simone Severini and Toufik Mansour, Enumeration of (k,2)-noncrossing partitions.
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EXAMPLE
| Table begins:
k|n|..0.....1.....2.....3.....4.....5.....6.....7.....8.....9......10.....11......12
.2|..1.....1.....2.....5....14....42...132...429..1430..4862...16796..58786..208012
.3|..1.....1.....2.....5....15....51...188...731..2950.12235...51822.223191..974427
.4|..1.....1.....2.....5....15....52...202...856..3868.18313...89711.450825.2310453
.5|..1.....1.....2.....5....15....52...203...876..4112.20679..109853.608996.3488806
.6|..1.....1.....2.....5....15....52...203...877..4139.21111..115219.666388.4045991
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CROSSREFS
| Rows include A000108, A007317, A140980, A141080, A141081.
Sequence in context: A151893 A000361 A135723 * A127568 A143364 A159046
Adjacent sequences: A125308 A125309 A125310 * A125312 A125313 A125314
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KEYWORD
| nonn,tabl
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 10 2006
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