a(n) = Sum_{k=0..n} (-1)^k * binomial(n+3*k+3,n-k) * Catalan(k).

Terms

a(0) =1a(1) =3a(2) =4a(3) =3a(4) =5a(5) =12a(6) =6a(7) =-13a(8) =29a(9) =95a(10) =-130a(11) =-304a(12) =895a(13) =1050a(14) =-5068a(15) =-2181a(16) =27743a(17) =-5481a(18) =-143532a(19) =117983a(20) =700831a(21) =-1074414a(22) =-3163138a(23) =7872784a(24) =12585117a(25) =-51587107a(26) =-38040886a(27) =312988334a(28) =18178883a(29) =-1779688404