

A125311


Array giving number of (k,2)noncrossing partitions of n, read by antidiagonals.


3



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
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OFFSET

0,6


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. [?verbatim from the paper?]


LINKS

Table of n, a(n) for n=0..35.
Toufik Mansour and Simone Severini, Enumeration of (k,2)noncrossing partitions, Discrete Math., 308 (2008), 45704577.


EXAMPLE

Table begins:
kn..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


CROSSREFS

Rows include A000108, A007317, A140980, A141080, A141081.
Sequence in context: A000361 A246596 A135723 * A127568 A263791 A327722
Adjacent sequences: A125308 A125309 A125310 * A125312 A125313 A125314


KEYWORD

nonn,more,tabl


AUTHOR

Jonathan Vos Post, Dec 10 2006


EXTENSIONS

Offset corrected by Joerg Arndt, Apr 18 2014


STATUS

approved



