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 A360717 #22 Mar 06 2023 13:49:13 %S A360717 0,1,6,33,185,1050,6027,35014,205326,1209375,7119860,41744703, %T A360717 243218703,1406685280,8073640785,45991600860,260131208396, %U A360717 1461591509805,8162196518322,45327133739245,250431036147285,1377169337010390,7540979990097191,41130452834689218,223528009015333050,1210753768099880875,6537995998163877312 %N A360717 Number of unordered pairs of self-avoiding paths whose sets of nodes are disjoint subsets of a set of n points on a circle; one-node paths are allowed. %C A360717 Although each path is self-avoiding, the different paths are allowed to intersect. %H A360717 Ivaylo Kortezov, <a href="http://www.wfnmc.org/journal.html">Sets of Paths between Vertices of a Polygon</a>, Mathematics Competitions, Vol. 35 (2022), No. 2, ISSN:1031-7503, pp. 35-43. %F A360717 a(n) = n*(n-1)*2^(-5)*(5^(n-2) + 6*3^(n-2) + 9). %F A360717 E.g.f.: exp(x)*((x*exp(2*x) + 3*x)/4)^2/2. - _Andrew Howroyd_, Feb 19 2023 %e A360717 a(4) = A359405(4) + 4*A359405(3) + 4*3/2 = 15 + 12 + 6 = 33 with the three summands corresponding to the cases of 4, 3 and 2 used points. %Y A360717 If there is only one path, we get A360715. If one-node paths are not allowed, we get A360716. %K A360717 nonn %O A360717 1,3 %A A360717 _Ivaylo Kortezov_, Feb 18 2023