a(n) = binomial(4*n-1, 2*n).

Terms

a(0) =1a(1) =3a(2) =35a(3) =462a(4) =6435a(5) =92378a(6) =1352078a(7) =20058300a(8) =300540195a(9) =4537567650a(10) =68923264410