a(n) = Catalan(n)^2*n.

Terms

a(0) =0a(1) =1a(2) =8a(3) =75a(4) =784a(5) =8820a(6) =104544a(7) =1288287a(8) =16359200a(9) =212751396a(10) =2821056160a(11) =38013731756a(12) =519227905728