Royal paths in a lattice (convolution of A006318).

Terms

a(0) =1a(1) =1a(2) =4a(3) =16a(4) =68a(5) =304a(6) =1412a(7) =6752a(8) =33028a(9) =164512a(10) =831620a(11) =4255728a(12) =22004292a(13) =114781008a(14) =603308292a(15) =3192216000a(16) =16989553668a(17) =90890869312a(18) =488500827908