From generalized Catalan numbers.

Terms

a(0) =1a(1) =8a(2) =52a(3) =320a(4) =1938a(5) =11704a(6) =70840a(7) =430560a(8) =2629575a(9) =16138848a(10) =99522896a(11) =616480384a(12) =3834669566a(13) =23944995480a(14) =150055305008a(15) =943448717120