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%I #9 Aug 28 2019 12:40:18
%S 2,14,107,844,6757,54522,441863,3589880,29206025,237780982,1936486411,
%T 15771410420,128431734797,1045618229234,8510270668815,69241255165936,
%U 563154350637073,4578526894227438,37209886138826771,302291556342169580
%N Number of rooted dual-unicursal 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)*A069720(n)-A103944(n).
%t A069720[n_] := 2^(n-1) Binomial[2n-1, n];
%t A103944[n_] := If[n == 1, 1, n Binomial[2n, n] Sum[Binomial[n-2, k] (1/(n + 1 + k) + n/(n + 2 + k)), {k, 0, n-2}]];
%t a[n_] := (n+2) A069720[n] - A103944[n];
%t Array[a, 20] (* _Jean-François Alcover_, Aug 28 2019 *)
%Y Cf. A069720, A103944.
%K easy,nonn
%O 1,1
%A _Valery A. Liskovets_, Mar 17 2005