a(n) = lcm(1,...,2n+4)/((n+1)*binomial(2n+2, n+1)).

Terms

a(0) =6a(1) =5a(2) =14a(3) =9a(4) =22a(5) =65a(6) =30a(7) =119a(8) =532a(9) =126a(10) =690a(11) =825a(12) =594a(13) =4147a(14) =62062a(15) =15015a(16) =3640a(17) =32708a(18) =7956a(19) =79458a(20) =833340a(21) =203490a(22) =2337874a(23) =4004231a(24) =980628a(25) =12738550a(26) =3124550a(27) =766935a(28) =11113830a(29) =166613265