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%I #18 Jan 22 2025 00:07:38
%S 1,2,5,18,70,323,1683,9690,59917,388894,2606742,17869870
%N Number of 'tree-like curves' with n intersection points.
%C The objects being enumerated are a subset of those enumerated by A008983. The restriction involved is that the Gauss diagram (or chord diagram) has no intersecting chords.
%D V. I. Arnold, Topological Invariants of plane curves and caustics, AMS, 1994, page 12.
%H Andrey Zabolotskiy, <a href="https://github.com/colt-browning/closed_curves">closed_curves</a> - a program computing the sequence (2025).
%e The first 3 entries are the same as A008983 because, for less than 3 intersection points, all curves are tree-like. For 3 intersection points there are only 2 curves that are not tree-like. They appear as the 4th and 15th entries in the table for n=3, on page 14 of Arnold's book.
%Y Cf. A008983.
%K nonn,more
%O 0,2
%A _Moshe Shmuel Newman_, May 23 2006
%E a(5)-a(11) from _Andrey Zabolotskiy_, Jan 16 2025