Certain directed lattice paths.

Terms

a(0) =1a(1) =3a(2) =15a(3) =84a(4) =491a(5) =2948a(6) =18018a(7) =111520a(8) =696739a(9) =4384668a(10) =27753110a(11) =176494640a(12) =1126809230a(13) =7217773800a(14) =46364184420a(15) =298554038144