Super ballot numbers: 6(2n)!/(n!(n+2)!).

Terms

a(0) =3a(1) =2a(2) =3a(3) =6a(4) =14a(5) =36a(6) =99a(7) =286a(8) =858a(9) =2652a(10) =8398a(11) =27132a(12) =89148a(13) =297160a(14) =1002915a(15) =3421710a(16) =11785890a(17) =40940460a(18) =143291610a(19) =504932340a(20) =1790214660a(21) =6382504440a(22) =22870640910a(23) =82334307276a(24) =297670187844