A Catalan-like sequence.

Terms

a(0) =0a(1) =1a(2) =4a(3) =11a(4) =36a(5) =115a(6) =381a(7) =1287a(8) =4420a(9) =15396a(10) =54264a(11) =193154a(12) =693373a(13) =2507287a(14) =9124560a(15) =33393355a(16) =122821380a(17) =453756765a(18) =1683107800a(19) =6265751310a(20) =23402516280a(21) =87670790155a(22) =329337229104