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

Terms

a(0) =1a(1) =1a(2) =3a(3) =11a(4) =42a(5) =162a(6) =627a(7) =2431a(8) =9438a(9) =36686a(10) =142766a(11) =556206a(12) =2169268a(13) =8469060a(14) =33096195a(15) =129454695a(16) =506793270a(17) =1985612310a(18) =7785510810a(19) =30548406570a(20) =119944382220a(21) =471241577820