Number of Motzkin trees that are "uniquely closable skeletons".

Terms

a(0) =0a(1) =1a(2) =0a(3) =1a(4) =1a(5) =2a(6) =2a(7) =7a(8) =5a(9) =20a(10) =19a(11) =60a(12) =62a(13) =202a(14) =202a(15) =679a(16) =711a(17) =2304a(18) =2507a(19) =8046a(20) =8856a(21) =28434a(22) =31855a(23) =101288a(24) =115596a(25) =364710a(26) =421654a(27) =1323946a(28) =1549090a(29) =4836072