Number of noncrossing caterpillars with n edges.

Terms

a(0) =1a(1) =1a(2) =3a(3) =12a(4) =55a(5) =273a(6) =1372a(7) =6824a(8) =33489a(9) =162405a(10) =779801a(11) =3713436a(12) =17560803a(13) =82553597a(14) =386105790a(15) =1797803248a(16) =8338313697a(17) =38539754649a(18) =177581276639a(19) =815982230060