Certain directed lattice paths.

Terms

a(0) =1a(1) =3a(2) =10a(3) =41a(4) =190a(5) =946a(6) =4940a(7) =26693a(8) =147990a(9) =837102a(10) =4811860a(11) =28027210a(12) =165057100a(13) =981177060a(14) =5879570200a(15) =35478788269a(16) =215398416870