A390907 Number of sets of noncrossing paths whose nodes are a subset of n nodes arranged in a circle with one node paths allowed.

1, 2, 5, 17, 75, 392, 2317, 15269, 111217, 885878, 7637889, 70724381, 699254467, 7346685140, 81675395449, 957180276833, 11786020254945, 152042198827658, 2049662488239325, 28809373453125545, 421333959129174811, 6399594458244765632, 100780831110223983525, 1642983996910638959357

Offset

0,2

Comments

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.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Formula

E.g.f.: exp(x + x*(exp(2*x + O(x^n)) + 3)/4).

Binomial transform of A390895.

Prog

(PARI) seq(n) = Vec(serlaplace( exp(x + x*(exp(2*x + O(x^n)) + 3)/4) ));

Crossrefs

Row sums of A390897.

Cf. A390895.

Sequence in context: A259870 A391652 A348878 * A118100 A129591 A328439

Adjacent sequences: A390904 A390905 A390906 * A390908 A390909 A390910

Keyword

nonn

Author

Andrew Howroyd, Nov 23 2025

Status

approved