A352367 Row sums of A352366.

1, 1, 2, 6, 23, 105, 552, 3276, 21632, 157058, 1241542, 10599358, 97078720, 948631866, 9844060930, 108045790170, 1249891268947, 15192207346713, 193489732812832, 2575819322454708, 35763019798305487, 516830453606687539, 7760160395056532042, 120860540786892879030

Offset: 0

Author

Peter Luschny, Mar 15 2022

Keywords

• nonn

Comments

a(n) is the number of chordal graphs with fixed symmetric perfect elimination ordering; i.e., graphs on V = [n] such that 1,...,n and n,...,1 are perfect elimination orderings. - Robert Lauff, Jan 25 2023

a(n) is the number of labeled unit-interval-graphs. This is because connected labeled unit-interval-graphs are a Catalan family. Given a partition of [n], we draw a connected unit-interval-graph for each of the partition classes. This weights the partitions with a Catalan number. The connection to my previous comment can be shown by induction. - Robert Lauff, Feb 01 2023

Links

• Wikipedia, Chordal graph.

Crossrefs

Cf. A000108, A352366.