a(n) = (5n+1)*C(4n,n)/(3n+1).

Terms

a(0) =1a(1) =6a(2) =44a(3) =352a(4) =2940a(5) =25194a(6) =219604a(7) =1937520a(8) =17250012a(9) =154663960a(10) =1394538288a(11) =12631852688a(12) =114858935204