%I A103941
%S A103941 1,2,6,22,103,614,3872,26414,186988,1367976,10254326,78461338,610598818,
%T A103941 4821248244,38546510368,311560875422,2542507084588,20925300483992,
%U A103941 173530381632724,1448900079476152
%N A103941 Number of unrooted loopless n-edge maps in the plane (planar with a distinguished 
               outside face).
%D A103941 V. A. Liskovets and T. R. Walsh, Enumeration of unrooted maps on the 
               plane, Rapport technique, UQAM, No. 2005-01, Montreal, Canada, 2005.
%H A103941 V. A. Liskovets and T. R. Walsh, <a href="http://dx.doi: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 A103941 a(n)=(1/(2n))[binomial(4n, n)/(3n+1) + sum_{0<k<n, k|n}phi(n/k)binomial(4k, 
               k)+q(n)] where phi is the Euler function A000010, q(n)=0 if n is 
               even and q(n)=binomial(2n, (n-1)/2) if n is odd.
%Y A103941 Cf. A002293, A103942, A000260, A005470.
%Y A103941 Sequence in context: A000140 A079263 A129815 this_sequence A064643 A129535 
               A014371
%Y A103941 Adjacent sequences: A103938 A103939 A103940 this_sequence A103942 A103943 
               A103944
%K A103941 easy,nonn
%O A103941 1,2
%A A103941 Valery A. Liskovets (liskov(AT)im.bas-net.by), Mar 17 2005