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A219587 Noncrossing, nonnesting, 2-arc-colored permutations on the set {1..n} where lower arcs even of different colors do not cross. 1
1, 2, 8, 40, 224, 1296, 7568, 44304, 259536, 1520656, 8910160, 52209040, 305919696, 1792542992, 10503446608, 61545189520, 360625475024, 2113093401616, 12381720203088, 72550979111824, 425114158957776, 2490966357221136, 14595875630354000, 85524874633320080 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The sequence is generated by a rational function, in particular, a quotient of two determinants.

LINKS

Lily Yen, Table of n, a(n) for n = 0..1000

Lily Yen, Crossings and Nestings for Arc-Coloured Permutations, arXiv:1211.3472

FORMULA

G.f.: (1 - 5x)/(1 - 7x + 6x^2 + 4x^3).

EXAMPLE

For n=4, the a(4) = 224 solutions are 24 permutations, 8 of which can be colored in 4 ways each, 8 in 8 ways each, and 8 in 16 ways each, thus resulting in 8 * (4+8+16) = 224.

CROSSREFS

Sequence in context: A027282 A006195 A214763 * A092807 A074601 A214760

Adjacent sequences:  A219584 A219585 A219586 * A219588 A219589 A219590

KEYWORD

nonn

AUTHOR

Lily Yen, Nov 23 2012

EXTENSIONS

Name modified by Lily Yen, Apr 23 2013

STATUS

approved

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Last modified March 21 12:12 EDT 2019. Contains 321369 sequences. (Running on oeis4.)