This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A225032 #30 Jan 31 2024 10:55:48 %S A225032 1,7,55,493,5029,57379,716443,9604345,136236937,2022864031, %T A225032 31180099711,495615409957,8079827006125,134488017925243, %U A225032 2276945808434659,39088515241450609,678651272689389073,11890942901283331255,209891714523969067207,3727004974842239659741 %N A225032 Non-crossing, non-nesting, 6-colored set partitions. %H A225032 Lily Yen, <a href="/A225032/b225032.txt">Table of n, a(n) for n = 0..99</a> %H A225032 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 A225032 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 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 A225032 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 A225032 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (63,-1589,20515,-142915,509549,-727767,1). %F A225032 G.f.: (1-56*x+1203*x^2-12364*x^3+60675*x^4-113540*x^5+x^6)/ (1-63*x+1589*x^2-20515*x^3+142915*x^4-509549*x^5+727767*x^6-x^7). %F A225032 a(n) = 63*a(n-1) - 1589*a(n-2) + 20515*a(n-3) - 142915*a(n-4) + 509549*a(n-5) - 727767*a(n-6) + a(n-7) for n>6. - _Colin Barker_, Jun 22 2019 %e A225032 For n=2, a(2)=55 is the number of non-crossing, non-nesting set partitions on 3 elements with 6 possible arc colors. %o A225032 (PARI) Vec((1 - 56*x + 1203*x^2 - 12364*x^3 + 60675*x^4 - 113540*x^5 + x^6) / (1 - 63*x + 1589*x^2 - 20515*x^3 + 142915*x^4 - 509549*x^5 + 727767*x^6 - x^7) + O(x^40)) \\ _Colin Barker_, Jun 22 2019 %K A225032 nonn,easy %O A225032 0,2 %A A225032 _Lily Yen_, Apr 25 2013