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

Terms

a(0) =1a(1) =10a(2) =84a(3) =715a(4) =6188a(5) =54264a(6) =480700a(7) =4292145a(8) =38567100a(9) =348330136a(10) =3159461968a(11) =28760021745a(12) =262596783764