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%I #20 Jan 17 2022 17:22:02
%S 1,5,121,4690,228065,12673173,768897585,49645423227,3357669088200,
%T 235393836387360,16981887962145418,1254065444086727685,
%U 94424981678123285373,7227272422780512414100,560989900421822288646265,44076648941211191411236261,3500015582480750626266664105
%N Number of corner-rooted pentagulations of girth 5 with 2n+1 inner faces.
%H Olivier Bernardi and Éric Fusy, <a href="https://doi.org/10.1016/j.jcta.2011.08.006">A bijection for triangulations, quadrangulations, pentagulations, etc</a>, Journal of Combinatorial Theory, Series A 119, 1 (2012) 218-244; arXiv:<a href="https://arxiv.org/abs/1007.1292">1007.1292</a> [math.CO], 2010-2011.
%H William G. Brown, <a href="https://doi.org/10.1112/plms/s3-14.4.746">Enumeration of Triangulations of the Disk</a>, Proc. Lond. Math. Soc. s3-14 (1964) 746-768.
%H William G. Brown, <a href="https://doi.org/10.4153/CJM-1965-030-1">Enumeration of quadrangular dissections of the disk</a>, Canad. J. Math., 17 (1965) 302-317.
%H W. T. Tutte, <a href="https://doi.org/10.4153/CJM-1963-029-x">A Census of Planar Maps</a>, Canad. J. Math. 15 (1963), 249-271.
%t k = 34;
%t {w0, w1, w2, w3} = FixedPoint[Function[{w0, w1, w2, w3}, {w1^2 + w2, w1^3 + 2 w1 w2 + w3, w1^4 + 3 w1^2 w2 + 2 w1 w3 + w2^2, x (1 + w0)^4} + O[x]^k] @@ # &, ConstantArray[0, 4]];
%t f = w3 - (w0 w3 + 2 w1 w2);
%t CoefficientList[f, x][[2 ;; ;; 2]]
%t (* _Andrey Zabolotskiy_, Jan 17 2022 *)
%Y Cf. A069271, A001764, A179300.
%K nonn
%O 0,2
%A _Jonathan Vos Post_, Jul 09 2010
%E Entry edited, terms a(5) and beyond added by _Andrey Zabolotskiy_, Jan 17 2022
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