A225031 Non-crossing, non-nesting, 5-colored set partitions.

1, 6, 41, 321, 2846, 27961, 297681, 3371646, 40065361, 494281201, 6279901766, 81649478161, 1080910639201, 14511820543126, 196956264035481, 2695543342918241, 37127978351861646, 513895401953712521, 7139331902125917361, 99462520534916445006, 1388616983941077336321

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 [math.CO], 2012-2013.

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-François 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 A345189 A083430

Adjacent sequences: A225028 A225029 A225030 * A225032 A225033 A225034

Keyword

nonn,easy

Author

Lily Yen, Apr 25 2013

Status

approved