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%I #16 Aug 28 2019 10:00:50
%S 1,2,9,38,214,1253,7925,51620,346307,2365886,16421359,115384738,
%T 819276830,5868540399,42357643916,307753571520,2249048959624,
%U 16520782751969,121915128678131,903391034923548,6719098772562182
%N Number of nonisomorphic unrooted unicursal planar maps with n edges (unicursal means that exactly two vertices are of odd valency; there is an Eulerian path).
%H G. C. Greubel, <a href="/A069724/b069724.txt">Table of n, a(n) for n = 1..1000</a>
%H V. A. Liskovets and T. R. S. Walsh, <a href="http://dx.doi.org/10.1016/j.disc.2003.09.015">Enumeration of Eulerian and unicursal planar maps</a>, Discr. Math., 282 (2004), 209-221.
%F There is an easy formula.
%F a(n) ~ 8^(n-1) / (sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Aug 28 2019
%t a[n_] := 1/(2 n) DivisorSum[n, If[OddQ[n/#], EulerPhi[n/#] 2^(#-2) Binomial[2 #, #], 0]&] + If[OddQ[n], 2^((n-3)/2) Binomial[n-1, (n-1)/2], 2^((n-6)/2) Binomial[n, n/2]]; Array[a, 21] (* _Jean-François Alcover_, Sep 18 2016 *)
%Y Cf. A069720, A069727, A005470.
%K easy,nice,nonn
%O 1,2
%A _Valery A. Liskovets_, Apr 07 2002
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