A225033 Non-crossing, non-nesting, 7-colored set partitions.
1, 8, 71, 715, 8212, 106205, 1514633, 23353828, 383455843, 6630981491, 119760987872, 2243989397161, 43378019032321, 861000869284928, 17476961860459151, 361541275664799595, 7599788958355060972, 161922899182197739685, 3489406153035009734633, 75917779229255330345308
Offset: 0
Keywords
Examples
For n=2, a(2)=71 is the number of non-crossing, non-nesting, 7-colored set partitions on 3 elements.
Links
- Muniru A Asiru, Table of n, a(n) for n = 0..150 (Terms n=0..99 from Lily Yen)
- 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, arXiv:1211.3472 [math.CO], 2012-2013; Formal Power Series and Algebraic Combinatorics Conference, June (2013), to appear.
- Lily Yen, Crossings and Nestings for Arc-Coloured Permutations and Automation, Electronic Journal of Combinatorics, 22(1) (2015), #P1.14.
Programs
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Maple
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
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Mathematica
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}]]; Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Feb 22 2019 *)
Formula
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).