A103944 - OEIS

%I #14 May 13 2013 01:30:57

%S 1,10,93,836,7355,63750,546553,4646920,39250935,329789450,2758868981,

%T 22995369996,191074697203,1583463268366,13092015636465,

%U 108024564809744,889730213085167,7316434446188562,60078376613838829,492692533579612180

%N Number of rooted 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 Vincenzo Librandi, <a href="/A103944/b103944.txt">Table of n, a(n) for n = 1..200</a>

%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*binomial(2n, n)sum_{i=0..n-2} binomial(n-2, i)(1/(n+1+i)+n/(n+2+i)), for n>1.

%F Recurrence: (n-1)*a(n) = 3*(3*n-4)*a(n-1) - 6*(n-9)*a(n-2) - 8*(2*n-5)*a(n-3). - _Vaclav Kotesovec_, Oct 17 2012

%F a(n) ~ 8^n*sqrt(n)/(6*sqrt(Pi)). - _Vaclav Kotesovec_, Oct 17 2012

%t Flatten[{1,Table[n*Binomial[2n,n]*Sum[Binomial[n-2,k]*(1/(n+1+k)+n/(n+2+k)),{k,0,n-2}],{n,2,20}]}] (* _Vaclav Kotesovec_, Oct 17 2012 *)

%Y Cf. A069720, A103945.

%K easy,nonn

%O 1,2

%A _Valery A. Liskovets_, Mar 17 2005