a(n) = binomial(4*n,n)*(2*n+1)/(3*n+1).

Terms

a(0) =1a(1) =3a(2) =20a(3) =154a(4) =1260a(5) =10659a(6) =92092a(7) =807300a(8) =7152444a(9) =63882940a(10) =574221648a(11) =5188082354a(12) =47073334100a(13) =428634152730