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%I #27 Jan 31 2024 10:56:51
%S 1,6,41,321,2846,27961,297681,3371646,40065361,494281201,6279901766,
%T 81649478161,1080910639201,14511820543126,196956264035481,
%U 2695543342918241,37127978351861646,513895401953712521,7139331902125917361,99462520534916445006,1388616983941077336321
%N Non-crossing, non-nesting, 5-colored set partitions.
%H Lily Yen, <a href="/A225031/b225031.txt">Table of n, a(n) for n = 0..99</a>
%H Eric Marberg, <a href="http://arxiv.org/abs/1203.5738">Crossings and nestings in colored set partitions</a>, arXiv preprint arXiv:1203.5738 [math.CO], 2012-2013.
%H Lily Yen, <a href="http://arxiv.org/abs/1211.3472">Crossings and Nestings for Arc-Coloured Permutations</a>, and <a href="https://doi.org/10.46298/dmtcs.2339">Arc-coloured permutations</a>, PSAC 2013, Paris, France, June 24-28, Proc. DMTCS (2013) 743-754.
%H Lily Yen, <a href="https://doi.org/10.37236/4080">Crossings and Nestings for Arc-Coloured Permutations and Automation</a>, Electronic Journal of Combinatorics, 22(1) (2015), #P1.14.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (41,-638,4701,-16398,21721,-1).
%F 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).
%e For n=2, a(2)=41 is the number of non-crossing, non-nesting set partitions on 3 elements with 5 possible arc colors.
%t LinearRecurrence[{41, -638, 4701, -16398, 21721, -1}, {1, 6, 41, 321, 2846, 27961}, 21] (* _Jean-François Alcover_, Jul 22 2018 *)
%o (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
%K nonn,easy
%O 0,2
%A _Lily Yen_, Apr 25 2013
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