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A225031 Non-crossing, non-nesting, 5-colored set partitions. 1
1, 6, 41, 321, 2846, 27961, 297681, 3371646, 40065361, 494281201, 6279901766, 81649478161, 1080910639201, 14511820543126, 196956264035481, 2695543342918241, 37127978351861646, 513895401953712521, 7139331902125917361, 99462520534916445006, 1388616983941077336321 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Lily Yen, Table of n, a(n) for n = 0..99

Eric Marberg, Crossings and nestings in colored set partitions, arXiv preprint arXiv:1203.5738, 2012.

Lily Yen, Crossings and Nestings for Arc-Coloured Permutations, and Arc-coloured permutations, PSAC 2013, Paris, France, June 24-28, Proc. DMTCS (2013) 743-754

Lily Yen, Crossings and Nestings for Arc-Coloured Permutations and Automation, Electronic Journal of Combinatorics, 22(1) (2015), #P1.14.

Index entries for linear recurrences with constant coefficients, signature (41,-638,4701,-16398,21721,-1).

FORMULA

G.f.: (1 -35*x +433*x^2 -2233*x^3 +4035*x^4 -x^5) / (1 -41*x +638*x^2 -4701*x^3 +16398*x^4 -21721*x^5 +x^6).

EXAMPLE

For n=2, a(2)=41 is the number of non-crossing, non-nesting set partitions on 3 elements with 5 possible arc colors.

MATHEMATICA

LinearRecurrence[{41, -638, 4701, -16398, 21721, -1}, {1, 6, 41, 321, 2846, 27961}, 21] (* Jean-Fran├žois Alcover, Jul 22 2018 *)

PROG

(PARI) Vec((1 -35*x +433*x^2 -2233*x^3 +4035*x^4 -x^5) / (1 -41*x +638*x^2 -4701*x^3 +16398*x^4 -21721*x^5 +x^6) + O(x^66)) \\ Joerg Arndt, Apr 27 2013

CROSSREFS

Sequence in context: A024078 A095177 A199553 * A307663 A083430 A005011

Adjacent sequences:  A225028 A225029 A225030 * A225032 A225033 A225034

KEYWORD

nonn,easy

AUTHOR

Lily Yen, Apr 25 2013

STATUS

approved

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Last modified September 25 16:45 EDT 2020. Contains 337344 sequences. (Running on oeis4.)