cp's OEIS Frontend

A225033 Non-crossing, non-nesting, 7-colored set partitions.

%I A225033 #28 Feb 23 2019 02:20:45
%S A225033 1,8,71,715,8212,106205,1514633,23353828,383455843,6630981491,
%T A225033 119760987872,2243989397161,43378019032321,861000869284928,
%U A225033 17476961860459151,361541275664799595,7599788958355060972,161922899182197739685,3489406153035009734633,75917779229255330345308
%N A225033 Non-crossing, non-nesting, 7-colored set partitions.
%H A225033 Muniru A Asiru, <a href="/A225033/b225033.txt">Table of n, a(n) for n = 0..150</a> (Terms n=0..99 from Lily Yen)
%H A225033 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 A225033 Lily Yen, <a href="http://arxiv.org/abs/1211.3472">Crossings and Nestings for Arc-Coloured Permutations</a>, arXiv:1211.3472 [math.CO], 2012-2013; Formal Power Series and Algebraic Combinatorics Conference, June (2013), to appear.
%H A225033 Lily Yen, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p14">Crossings and Nestings for Arc-Coloured Permutations and Automation</a>, Electronic Journal of Combinatorics, 22(1) (2015), #P1.14.
%F A225033 G.f.: (1-84*x +2849*x^2 -49873*x^3 +474601*x^4 -2324333*x^5 +4567788*x^6 -x^7) / (1-92*x +3514*x^2 -72168*x^3 +860019*x^4 -5943768*x^5 +22055962*x^6 -33922100*x^7 +x^8).
%e A225033 For n=2, a(2)=71 is the number of non-crossing, non-nesting, 7-colored set partitions on 3 elements.
%p A225033 seq(coeff(series((1-84*x +2849*x^2 -49873*x^3 +474601*x^4 -2324333*x^5 +4567788*x^6 -x^7) / (1-92*x +3514*x^2 -72168*x^3 +860019*x^4 -5943768*x^5 +22055962*x^6 -33922100*x^7 +x^8),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Feb 22 2019
%t A225033 a = DifferenceRoot[Function[{a, n}, {a[n] - 33922100*a[n+1] + 22055962*a[n+2] - 5943768*a[n+3] + 860019*a[n+4] - 72168*a[n+5] + 3514*a[n+6] - 92*a[n+7] + a[n+8] == 0, a[0] == 1, a[1] == 8, a[2] == 71, a[3] == 715, a[4] == 8212, a[5] == 106205, a[6] == 1514633, a[7] == 23353828}]];
%t A225033 Table[a[n], {n, 0, 19}] (* _Jean-François Alcover_, Feb 22 2019 *)
%K A225033 nonn
%O A225033 0,2
%A A225033 _Lily Yen_, Apr 25 2013