A Catalan-like sequence.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =12a(5) =36a(6) =116a(7) =382a(8) =1287a(9) =4420a(10) =15397a(11) =54264a(12) =193154a(13) =693374a(14) =2507288a(15) =9124560a(16) =33393355a(17) =122821380a(18) =453756765a(19) =1683107800a(20) =6265751310a(21) =23402516280a(22) =87670790155a(23) =329337229104