a(n) = 3*binomial(7*n+3, n)/(7*n+3).

Terms

a(0) =1a(1) =3a(2) =24a(3) =253a(4) =3045a(5) =39627a(6) =543004a(7) =7718340a(8) =112752783a(9) =1682460520a(10) =25533901536a(11) =392912889915