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

Terms

a(0) =3a(1) =20a(2) =105a(3) =504a(4) =2310a(5) =10296a(6) =45045a(7) =194480a(8) =831402a(9) =3527160a(10) =14872858a(11) =62403600a(12) =260757900a(13) =1085822640a(14) =4508102925a(15) =18668849760a(16) =77138650050a(17) =318107374200