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Number of connected outerplanar graphs on n labeled nodes.
6

%I #12 Feb 12 2021 19:43:20

%S 1,1,1,4,37,602,14436,458062,18029992,845360028,45938606320,

%T 2836966508216,196156795008384,15008752290350656,1258841795197091392,

%U 114838947237881287800,11319937495659268412416,1198945386491423345685968,135784713567893046210563328

%N Number of connected outerplanar graphs on n labeled nodes.

%H Andrew Howroyd, <a href="/A097998/b097998.txt">Table of n, a(n) for n = 0..200</a>

%H M. Bodirsky and M. Kang, <a href="http://www.informatik.hu-berlin.de/~bodirsky/publications/asymptoticBK.html">The asymptotic number of outerplanar graphs</a>.

%H S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Planar graph growth constants</a>.

%H Steven R. Finch, <a href="/A097999/a097999.pdf">Planar graph growth constants</a> [Cached copy, with permission of the author]

%F Recurrence known, see Bodirsky and Kang.

%o (PARI) seq(n)={Vec(serlaplace(1 + intformal(serreverse(x/exp((1 + 5*x - sqrt(1 - 6*x + x^2 + O(x^n)))/8))/x)))} \\ _Andrew Howroyd_, Feb 12 2021

%Y Cf. A097999, A098000, A111563.

%K nonn

%O 0,4

%A _Steven Finch_, Sep 08 2004

%E a(0)=1 prepended and terms a(17) and beyond from _Andrew Howroyd_, Feb 12 2021