a(n) = (2*n+3)!/(6*n!*(n+1)!).

Terms

a(0) =1a(1) =10a(2) =70a(3) =420a(4) =2310a(5) =12012a(6) =60060a(7) =291720a(8) =1385670a(9) =6466460a(10) =29745716a(11) =135207800a(12) =608435100a(13) =2714556600a(14) =12021607800a(15) =52895074320a(16) =231415950150