A098000 Number of outerplanar graphs on n labeled nodes.

1, 1, 2, 8, 63, 893, 19714, 597510, 22903403, 1056115331, 56744710974, 3475626211316, 238818544070905, 18183183610029003, 1519020289266947462, 138117136134012654182, 13576724206357958780409, 1434561741418662640589225, 162136032834834405685977058, 19516966563322659948894106704

Offset: 0

Author

Steven Finch, Sep 08 2004

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• M. Bodirsky and M. Kang, The asymptotic number of outerplanar graphs.
• S. R. Finch, Planar graph growth constants.
• Steven R. Finch, Planar graph growth constants [Cached copy, with permission of the author]

Crossrefs

Cf. A097998, A097999, A111564, A005470.

Programs

PARI

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

Formula

Recurrence known, see Bodirsky and Kang.

Exponential transform of A097998. - Andrew Howroyd, Feb 12 2021

Extensions

a(0)=1 prepended and terms a(17) and beyond from Andrew Howroyd, Feb 12 2021