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%I M1977 #36 Feb 19 2024 01:35:37
%S 1,2,10,83,690,6412,61842,617025,6302725,65619820,693643860,
%T 7425181257,80326705270,876832043840,9645743783040,106827450870525,
%U 1190150414448795,13329010510209790,149976822229984908,1694617702395672670,19220402733369657820
%N Number of planar 2-trees with n nodes.
%C Table 2 of Palmer and Read paper gives incorrect value a(10) = 457025. - _Sean A. Irvine_, Feb 12 2016
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Allan Bickle, <a href="https://doi.org/10.20429/tag.2024.000105">A Survey of Maximal k-degenerate Graphs and k-Trees</a>, Theory and Applications of Graphs 0 1 (2024) Article 5.
%H E. M. Palmer and R. C. Read, <a href="https://doi.org/10.1112/jlms/s2-6.4.583">On the number of plane 2-trees</a>, J. Lond. Math. Soc., 6 (1973), 583-592.
%H E. M. Palmer and R. C. Read, <a href="/A003093/a003093.pdf">On the number of plane 2-trees</a>, J. Lond. Math. Soc., 6 (1973), 583-592. [Annotated and corrected scanned copy]
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F G.f.: P(x) + (1/2) * x^2 * ((1 - T(x^2))^(-1) - 1) + (2/3) * x^3 * (1 - T(x^3))^(-2) where P(x) = Sum_{k>=1} ((k * (k - 1) * (5*k-10)! / (4*k-6)!) * x^k / k!) is the e.g.f. of A003092 and T(x) = Sum_{k>=1} (((5 * k - 2)!/ (4 * k - 1)!) * x^k / k!) is the e.g.f. of A120348. - _Sean A. Irvine_, Feb 12 2016
%Y Cf. A003092, A120348.
%K nonn
%O 3,2
%A _N. J. A. Sloane_
%E a(10) corrected and more terms from _Sean A. Irvine_, Feb 12 2016
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