a(n) = binomial(3*n+1,n)/(n+1).

Terms

a(0) =1a(1) =2a(2) =7a(3) =30a(4) =143a(5) =728a(6) =3876a(7) =21318a(8) =120175a(9) =690690a(10) =4032015a(11) =23841480a(12) =142498692a(13) =859515920a(14) =5225264024a(15) =31983672534a(16) =196947587823