A Catalan-related transform of 3^n.

Terms

a(0) =1a(1) =3a(2) =9a(3) =30a(4) =99a(5) =330a(6) =1098a(7) =3660a(8) =12195a(9) =40650a(10) =135486a(11) =451620a(12) =1505358a(13) =5017860a(14) =16726068a(15) =55753560a(16) =185844771a(17) =619482570a(18) =2064940470a(19) =6883134900a(20) =22943778138a(21) =76479260460a(22) =254930851404a(23) =849769504680