a(n) = 3*binomial(5n+2,n)/(4n+3).

Terms

a(0) =1a(1) =3a(2) =18a(3) =136a(4) =1155a(5) =10530a(6) =100688a(7) =996336a(8) =10116873a(9) =104819165a(10) =1103722620a(11) =11777187240a(12) =127067830773