The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #5 Nov 23 2025 16:29:26
%S 1,2,5,17,75,392,2317,15269,111217,885878,7637889,70724381,699254467,
%T 7346685140,81675395449,957180276833,11786020254945,152042198827658,
%U 2049662488239325,28809373453125545,421333959129174811,6399594458244765632,100780831110223983525,1642983996910638959357
%N Number of sets of noncrossing paths whose nodes are a subset of n nodes arranged in a circle with one node paths allowed.
%C Each path consists of straight line segments connecting one or more nodes on the circle. Each of the n nodes is used by at most one path. Although each path is noncrossing, different paths are allowed to intersect.
%H Andrew Howroyd, <a href="/A390907/b390907.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: exp(x + x*(exp(2*x + O(x^n)) + 3)/4).
%F Binomial transform of A390895.
%o (PARI) seq(n) = Vec(serlaplace( exp(x + x*(exp(2*x + O(x^n)) + 3)/4) ));
%Y Row sums of A390897.
%Y Cf. A390895.
%K nonn
%O 0,2
%A _Andrew Howroyd_, Nov 23 2025