Linear recursion with Catalan numbers.

Terms

a(0) =2a(1) =9a(2) =32a(3) =115a(4) =420a(5) =1554a(6) =5808a(7) =21879a(8) =82940a(9) =316030a(10) =1209312a(11) =4644094a(12) =17889032a(13) =69089700a(14) =267444000a(15) =1037348415a(16) =4030774380a(17) =15687019590a(18) =61137753600a(19) =238580530650a(20) =932105099640