Royal paths in a lattice.

Terms

a(0) =1a(1) =6a(2) =30a(3) =146a(4) =714a(5) =3534a(6) =17718a(7) =89898a(8) =461010a(9) =2386390a(10) =12455118a(11) =65478978a(12) =346448538a(13) =1843520670a(14) =9859734630a(15) =52974158938a(16) =285791932578