%I
%S 1,2,13,213,7584,454380,39665160,4775586480
%N Number of ways to lace a shoe that has n pairs of eyelets such that each eyelet has at least one direct connection to the opposite side.
%C The lace is "undirected": reversing the order of eyelets along the path does not count as a different solution. It must begin and end at the extreme pair of eyelets,
%H <a href="/index/La#lacings">Index entries for sequences related to shoe lacings</a>
%e a(3) = 13: label the eyelets 1,2,3 from front to back on the left side then 4,5,6 from back to front on the right side. The lacings are: 124356 154326 153426 142536 145236 135246 125346 124536 125436 152346 153246 152436 154236.
%Y Cf. A078698, A078700, A078675.
%Y a(n) = ( A078698(n) + A078700(n) ) / 2
%K nonn
%O 1,2
%A _Hugo Pfoertner_, Dec 18 2002
