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%I #19 Feb 09 2022 09:05:49
%S 3,2,5,18,77,364,1836,9690,52877,296010,1690845,9817080,57769740,
%T 343806368,2065802056,12515350122,76367432013,468922828150,
%U 2895381678735,17966214519330,111977263221285,700704492237540,4400559613086000,27727270719559320,175230257041962252
%N Number of rooted non-separable n-edge maps in the plane (planar with a distinguished outside face).
%D V. A. Liskovets and T. R. Walsh, Enumeration of unrooted maps on the plane, Rapport technique, UQAM, No. 2005-01, Montreal, Canada, 2005.
%H V. A. Liskovets and T. R. Walsh, <a href="http://dx.doi.org/10.1016/j.aam.2005.03.006">Counting unrooted maps on the plane</a>, Advances in Applied Math., 36, No.4 (2006), 364-387.
%F a(n) = (n+2)*A000139(n)/2.
%F From _Peter Bala_, Feb 07 2022: (Start)
%F a(n) = 4*A001764(n-1) - A006013(n-1).
%F a(n) = (3*n+6)*(3*n-4)*(3*n-5)/(n*(2*n-1)*(2*n+2))*a(n-1).
%F O.g.f.: A(x) = x*T(x)*(4 - T(x)), where T(x) = 1 + x*T(x)^3 is the g.f. of A001764. (End)
%t a[n_] := (n+2)(3(n-1))!/((2n-1)! n!);
%t Array[a, 30] (* _Jean-François Alcover_, Aug 29 2019 *)
%Y Cf. A000139, A001764, A006013.
%K nonn,easy
%O 1,1
%A _Valery A. Liskovets_, Mar 17 2005
%E More terms from _Jean-François Alcover_, Aug 29 2019
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