a(n) = binomial(4*n,n)/4.

Terms

a(0) =1a(1) =7a(2) =55a(3) =455a(4) =3876a(5) =33649a(6) =296010a(7) =2629575a(8) =23535820a(9) =211915132a(10) =1917334783a(11) =17417133617a(12) =158753389900