a(n) = (n+1)^2*binomial(2*n+2,n-1)/2.

Terms

a(0) =0a(1) =2a(2) =27a(3) =224a(4) =1500a(5) =8910a(6) =49049a(7) =256256a(8) =1288872a(9) =6298500a(10) =30093910a(11) =141210432a(12) =652860520a(13) =2981331990a(14) =13472983125a(15) =60343756800a(16) =268187306640